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

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Question 870785: Could you please help me prove the following mathematical statement.
Let p be a prime number and a and b positive integers, such that p/ab. then p/a or p/b.

Click here to see answer by richard1234(7193)

Question 870143: I need help with this question please.
If p is a prime number and ɸ is the Euler phi function.
Prove that ɸ(p) = p - 1

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Question 871305: Find the prime factorization of :
7^4 x 2 x 6^5 + 7^8 x 6^6

Click here to see answer by Edwin McCravy(20054)

Question 871318: A census taker stopped at a Hotel Sleep-Inn. The clerk at the desk was a mathematics student with a sense of humor. When asked how many guests were in the hotel, she replied, " The number is the smallest positive integer that has the following properties:
When divided by two, the result is a perfect square:
When divided by three, the result is a perfect cube."
Can you figure out how many guests were in the hotel?
Click here to see answer by Edwin McCravy(20054)

Question 871316: When the accountants for Lose-a-digit Computer, Inc. had finished preparing their annual budget, they presented the final figures to the president, I.M. Smart. "It looks like a good year," he exclaimed. "The amount of the budget just happens to be the smallest number of cents (other than one cent) that is a perfect square, a perfect cube, and a perfect fifth power." How much money has Lose-a digit budgeted for the year?
Click here to see answer by Edwin McCravy(20054)

Question 871159: I would appreciate help with this question please.
Checking to see whether the number p is prime or not.
Is it enough to test that p does not have any divisors ≤ square root of p.

Click here to see answer by Edwin McCravy(20054)

Question 871518: find the number of integers smaller than and are relatively prime to 80
Click here to see answer by Edwin McCravy(20054)

Question 858420: 34% of 18=
Click here to see answer by Edwin McCravy(20054)

Question 871554: find the number of factors of 500
which are divisible by 24
Click here to see answer by Fombitz(32388)

Question 872363: consider the equation x^2+y^2=2007 .how many solutions(x,y) exist such that x and y are positive integers?
A. NONE
B. EXACTLY TWO
C. MORE THAN TWO BUT FINITELY MANY
D. INFINITELY MANY
Click here to see answer by Edwin McCravy(20054)

Question 874305: Use multiples of the larger number to find the least common multiple in the set of 35 and 91? Please I need help?
Click here to see answer by josgarithmetic(39613)

Question 874305: Use multiples of the larger number to find the least common multiple in the set of 35 and 91? Please I need help?
Click here to see answer by MathTherapy(10549)

Question 874539: I am having a problem solving a riddle.
Here is the riddle.
I am a number less than 345
and greater than 340
I have two 1
What number am I
Click here to see answer by josgarithmetic(39613)

Question 877519: how many ordered pairs (x,y) of integers are solutions to xy/x+y = 24?
Click here to see answer by Edwin McCravy(20054)

Question 879959: find the difference (simply answer but do not factor)
x^2 -9
-2x^2+2x-2
______________

the negative 9 sits above the negative 2
Click here to see answer by ewatrrr(24785)

Question 881037: in an examination a student score 4 mark for every correct ans and lose 1 mark for every wrong ans if he attempts in all 60 question and secures 130 mark what no of question does he attempts correctly.
Click here to see answer by sl.ahmed(1)

Question 809425: Classify each of the following as true or false:
(a) If a number is divisible by 6, then it is divisible by 2 and 3.
(b) If a number is divisible by 2 and 3, then it is divisible by 6.
(c) If a number is divisible by 2 and 4, then it is divisible by 8.
(d) If a number is divisible by 8, then it is divisible by 2 and 4.

Click here to see answer by richwmiller(17219)

Question 857370: A carpenter undertakes to supply 2000 tables at Rs. 17.25 each. He estimates that if 10% are defective which will be sold at 50%, then the profit will be 15% on his whole outlay. When the tables were supplied 70% of the tables were found defective. What loss did the carpenter incur ?
Click here to see answer by richwmiller(17219)

Question 882462: find the least 5 digit number which is exactly divisible by 65

Click here to see answer by richard1234(7193)

Question 882496: Use the remainder theorem to find the remainder of (x^4-2x-4)/(x+1)
Click here to see answer by ewatrrr(24785)

Question 883788: how many numbers between 600 and 200 are divisible by 4,5,6?

Click here to see answer by Edwin McCravy(20054)

Question 883933: 6*3*a=an even number.
What is a?
1. an even number 2. an odd or even number
3. an odd number 4. divisible by 3
Click here to see answer by Alan3354(69443)

Question 885302: 2. How many multiples of 11 are there between 200 and 500?
a. 25 b. 26 c. 27 d. 28

Click here to see answer by Theo(13342)

Question 885563: 58/3
Click here to see answer by Alan3354(69443)

Question 886294: 3/5+ 4/15=?
Click here to see answer by rfer(16322)

Question 886625: Find the total no. of prime number factors in this expression

Click here to see answer by Edwin McCravy(20054)

Question 887515: When the positive whole number p is divided by 9 the remainder is 7 what is the remainder when p is divided by 5
Click here to see answer by rothauserc(4718)

Question 887110: consider the following statements:
A number a1a2a3a4a7 is divisible by 9 if
1.a1+a2+a3+a4+a7 is divisible by9.
2.a1-a2+a3-a4+a7 is divisible by 9.
which of the above statements is correct?
a.1 only.
b.2 only.
c. both 1 and 2.
Click here to see answer by Edwin McCravy(20054)

Question 888192: if (a/b)= 0.632 what is a+b
Click here to see answer by richwmiller(17219)

Question 888582: PPPPPLLLLLEEEEAASSSSEEE HELP!
-2 +7b <= -58
solve the inequality is the answer sign switched since multiplying by negative????
Click here to see answer by richwmiller(17219)

Question 889262: from left to right the first three digits of a 4- digits number add up to 14 . which digit could be in the ones place if the 4- digit numbers divisible by 3 ?
Click here to see answer by MathTherapy(10549)

Question 890712: determine the two numbers nearest to 10000 which are exactly divisible by each of 2,3,4,5,6 and 7

Click here to see answer by richwmiller(17219)

Question 891232: the smallest square number which is exactly divisible by 2,3,4,-9,6,18,36,60.
A.900
B.1600
C.3600
D.none of these
Click here to see answer by Fombitz(32388)

Question 891294: Find the least number divisible by each natural number less than or equal to 12
Click here to see answer by Fombitz(32388)

Question 891851: Select and perform an operation to the question.
1. What is the quotient of -21 and -7/3

Write in increasing order.
2. 2, -3/7, 0.75, -3/2
Click here to see answer by Alan3354(69443)

Question 892364: Prove : Two numbers when divided by a certain divisior give remainders r1 and r2. When their sum is divided by the same divisor, the remainder is r3. The divisor is given by r1 + r2 - r3
Click here to see answer by richard1234(7193)

Question 893007: How many integers are there between 1-199 that are divisible by both 4 and 5?

Click here to see answer by josgarithmetic(39613)

Question 893235: 6 power 71+6power 72 + 6 power 73 + 6 power 74 is completely divisible by
a) 103 b) 163 c ) 193
Click here to see answer by Alan3354(69443)

Question 894550: determine the two numbers nearest to 10000 which are exactly divisible by 2,3,4,5,6 and 7
Click here to see answer by josgarithmetic(39613)

Question 894550: determine the two numbers nearest to 10000 which are exactly divisible by 2,3,4,5,6 and 7
Click here to see answer by MathTherapy(10549)

Question 895047: aye yah there? do this for me "(6t+3(1-2t)-5" I is now how to do. tank you
Click here to see answer by josgarithmetic(39613)

Question 895224: 67^67+67 divided by 68 what will be reminder
Click here to see answer by Edwin McCravy(20054)

Question 895224: 67^67+67 divided by 68 what will be reminder
Click here to see answer by richard1234(7193)

Question 896751: if product of three prime numbers is 130 then what is their sum?
Click here to see answer by rothauserc(4718)

Question 899115: what are some exponents that the answer is between 130 and 120
Click here to see answer by richwmiller(17219)

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