Questions on Algebra: Divisibility and Prime Numbers answered by real tutors!

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Question 14277: This is the way the teacher wrote down the factorization of 36. (But shouldn't the factorization in the diagram be in the correct factor order of 2x2x3x3 and NOT 3x2x3x2 ?)
Why not:
....MY WAY....................TEACHER'S WAY
......36................................36..........
....../\................................./\.........
...4..X..9..........................6..X..6.........
..../\..../\.........................../\..../\.....
..2x2..X.3x3.......................3x2..X..3x2......
..2X2X3X3...........................2X2X3X3.........
Wouldn't this MY way be correct also?
My son and I are having a problem with diagramming a prime factorization 'tree' (tree is the name given for the drawing). When I diagram a whole number to get its factors, how can I tell what number I should start our with first in the diagram? e.g. MY WAY started with '4'. When I (mom) asked the teacher to send home how to do the tree, her tree started with '2' FIRST (see below). How do I figure out what number the tree diagram should start with underneath the whole number? Is there a specific rule to follow?

Whole number 120 was a problem my son had for homework last night (10/06/05-Thurs). He has a test on this subject Tuesday, 10/11/05 and he still doesn't understand how to do the tree, nor do I know how to help him.

According to a prime factorization chart 120 = 2x2x2x3x5.) Since its very hard to memorize such a listing, how do I know to start my diagram with the number '2'? Why not start with numbers: 120, then underneath, 6 x 20? Then under the 20 would go.... I know know??
PLEASE HELP---A mom who has been out of school since 1974!
Click here to see answer by atif.muhammad(135)

Question 14276: This is the way the teacher wrote down the factorization of 36. (But shouldn't the factorization in the diagram be in the correct factor order of 2x2x3x3 and NOT 3x2x3x2 ?)
Why not:
....MY WAY....................TEACHER'S WAY
......36................................36..........
....../\................................./\.........
...4..X..9..........................6..X..6.........
..../\..../\.........................../\..../\.....
..2x2..X.3x3.......................3x2..X..3x2......
..2X2X3X3...........................2X2X3X3.........
Wouldn't this MY way be correct also?
My son and I are having a problem with diagramming a prime factorization 'tree' (tree is the name given for the drawing). When I diagram a whole number to get its factors, how can I tell what number I should start our with first in the diagram? e.g. MY WAY started with '4'. When I (mom) asked the teacher to send home how to do the tree, her tree started with '2' FIRST (see below). How do I figure out what number the tree diagram should start with underneath the whole number? Is there a specific rule to follow?

Whole number 120 was a problem my son had for homework last night (10/06/05-Thurs). He has a test on this subject Tuesday, 10/11/05 and he still doesn't understand how to do the tree, nor do I know how to help him.

According to a prime factorization chart 120 = 2x2x2x3x5.) Since its very hard to memorize such a listing, how do I know to start my diagram with the number '2'? Why not start with numbers: 120, then underneath, 6 x 20? Then under the 20 would go.... I know know??
PLEASE HELP---A mom who has been out of school since 1974!
Click here to see answer by longjonsilver(2297)

Question 12939: How do you factor this?:

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Question 14801: what is 36 as a product of prime numbers?
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Question 15246: find 3 consecutive even integers such that the sum of the first three is 24 more than the fourth
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Question 10037: If n is an odd integer, which expression always represents an odd integer?
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Question 17726: I'm trying to help my son, 6th grade, with his home work. Could use any help you have to offer.
When multiplying the greatest common factor (GCF) and the least common multiple (LCM) of two numbers the product is always equal to the product of the original two numbers. Why?
Is there an easy to say theorem or "rule" that you could share.
What we came up with: The least commom multiple and the greatest common factor are common to the two numbers. Because they are the smallest and the largest common numbers, when they are multiplied their product is equal to the product of the original two numbers.
Click here to see answer by ivy12003(22)

Question 18104: Need help with 6th grade school project.Other students have to guess the secret number each clue must begin with "I am" and end with "Who am I?"
Example:

Who am I?
I am a composite number, but I look prime.
I am less than 60.
The sum of my digits is 6.
I am divisible by 17.
Who am I?
Click here to see answer by pwac(253)

Question 18692: What is the smallest prime factor of 1821
Click here to see answer by venugopalramana(3286)

Question 19023: Does there exist a two-digit number 'ab' such that the difference between 'ab' and its reverse 'ba' is a prime number?
Click here to see answer by MelanieBCC(40)

Question 20052: I can't seem to find the prime factorization of 1,120 can you help??????????????????????????????????????????????????????
Click here to see answer by elima(1433)

Question 20179: HOw many distinct prime numbers are factors of 70?
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Question 20179: HOw many distinct prime numbers are factors of 70?
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Question 20317: what are all the prime numbers?
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Question 20523: the number 64 is divisible by which of the following?
a.6 b.3
c.4 d.5
Click here to see answer by kcrawford(3)

Question 20524: choose a tens digit for 2?6 so that the three-digit number is divisible by 6.
a.1 b.3
c.2 d.0
Click here to see answer by Earlsdon(6294)

Question 21405: how do I simplify -6-(-3)+ 5-8
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Question 21405: how do I simplify -6-(-3)+ 5-8
Click here to see answer by queenofit(120)

Question 21792: How many factors, including 1, does the product of the first 9 primes divided by the product of the first seven primes have? I think the answer is 7
Click here to see answer by AnlytcPhil(1806)

Question 21796: What is the sum of the digits used to form the integers from 45 to 100 , inclusive?
I thought it was 45+55
Click here to see answer by AnlytcPhil(1806)

Question 23233: How many subsets of 3 different integers are there whose sum is divisiable by 4?
Click here to see answer by stanbon(75887)

Question 18148: Is there any square number besides 9 and 81 that is divisible by 9?
-Thanks!
Click here to see answer by kev82(151)

Question 25693: Do you have a list of prime numbers up to 1000?
Click here to see answer by Earlsdon(6294)

Question 25223: 26,65 what is the greatest common factor

Click here to see answer by venugopalramana(3286)

Question 27437: What number has only eleven factors?
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Question 27947: factors of 28
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Question 28412: how do you figure out the factors of a number and how do you know if it is prime or not?
Click here to see answer by longjonsilver(2297)

Question 29141: Find the prime factorization of 40
Click here to see answer by Earlsdon(6294)

Question 29141: Find the prime factorization of 40
Click here to see answer by atif.muhammad(135)

Question 29141: Find the prime factorization of 40
Click here to see answer by Nate(3500)

Question 29117: hi. i was assigned to show that there are 43411 consequtive composite numbers. ok, i know that i can do 43411! and if i`ll divide the whole thing by,
say n!+3 I`d be left with the composites. or should i do n! +1 but to start dividing from 43410! instead? thanks.
Click here to see answer by venugopalramana(3286)

Question 30515: -17+r=12
Click here to see answer by checkley71(8403)

Question 32007: Express 54 as a product of prime numbers.
Click here to see answer by venugopalramana(3286)

Question 32082: A whole number is divisible by 3 if the sum of its digits is divisible by 3?
Click here to see answer by Earlsdon(6294)

Question 32303: if T =3ph +5 Find T when p =4 and h = 2
Click here to see answer by mukhopadhyay(490)

Question 32496: we need an example of primefactorization.
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Question 32497: primefactorization...............the problem is...............52
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Question 32654: with the number 18 which number is divisible by 2, 3, 5, 9, or 10.

Click here to see answer by Earlsdon(6294)

Question 33205: 30 can be divided by ?
Click here to see answer by piglet162431(90)

Question 33245: 1. What is the prime factorization of 598?
2. Choose the correct statement? 12 is a factor of 4; 30 is a factor of 7; 7 is a factor of 30; 4 is a factor of 12.
3. Which of the following shows a pair of prime numbers? 21,33; 21,59; 59,73; 33,73.
4. Write the prime factorization of 120?
5. Which of the following numbers is not composite? 31,39, 35, 27
6. Determine the prime factorization of 3960?
7. What is a factor of 40?
8. What is a factor of 12?
9. Which is not a factor of 12? 3, 24, 4, 6
10. Which of the following numbers is prime? 51, 57, 97, 27
11. Which is not a factor of 48? 12, 24, 96, 16
12. Write 900 as a product of primes?
13. Write 2016 as a product of primes?
14. Which of the following numbers is prime? 15, 21, 83, 25
15. Which of the following numbers is prime? 10, 3, 21, 4
Click here to see answer by longjonsilver(2297)

Question 34044: one quart of paint is exactly enough for two coats of paint on a 9foot by 10 foot wall how many quarts of paint are needed to apply one quart of paint to a 10 foot by 12 foot wall?
Click here to see answer by mukhopadhyay(490)

Question 16846: What is the divisibility of 126?
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Question 16846: What is the divisibility of 126?
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Question 36003: factor the quadratic expression completely, and find the roots of the expression.
20x^2 + 13x + 2
Click here to see answer by checkley71(8403)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295