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

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 Question 1408: what the freak is the l.c.m AND the g.c.d. of 82, 96 and 112? i'm too tired to try this anymore! Thanks! Click here to see answer by AnlytcPhil(1321)

 Question 1833: tell me the method of how to find square root of a number by prime factorisation method eg of 576 Click here to see answer by longjonsilver(2297)

 Question 2634: a cook cuts a cake into 35 equal pieces and an identical cake into 42 pieces. The caterer, however, insists that the cakes be cut exactly alike. Into how many pieces must each cake now be cut Click here to see answer by khwang(438)

 Question 3015: I need step by step instructions on how to factor numbers and examples also. Click here to see answer by BestTutorEver(3)

 Question 3299: what is the largest prime less than 500? Click here to see answer by drglass(89)

 Question 3334: hi all what are the diffrences between pseudoprimes, strong pseudoprimes and carmicheal numbers? Click here to see answer by longjonsilver(2297)

 Question 3426: if 3 is the greatest common divisor of positive integers r and s, what is the greatest common divisor of 2r and 2s? (A) 2 (B) 3 (C) 4 (D) 6 (E) 12 Click here to see answer by khwang(438)

 Question 4388: I am having a lot of trouble with these proofs; I get so far and alskdjfl.... prove or give a counterexample: if a and b are integers such that 6 divides both a+b and a-b, then 3 divides both a and b. Show that the third power of every integer that is not divisible by 7 is of the form 7k+1 or 7k-1 where k is an integer. Prove: if n is an integer, then one of the integers n, n+2, and n+4 is divisible by 3. Use it to show that n=3 is the only integer such that n, n+2, and n+4 are primes. Prove or give a counterexample: if d=(a,b), then 3d=(3a,3b) Prove or give a counterexample: if a and b are integers such that a^2 divides b^3, then a divides b. Prove or give a counterexample: if the product of two integers is divisible by 3, then at least one of the integers is divisible by 3. Click here to see answer by khwang(438)

 Question 4648: Let p be prime. Prove that... (1 + p)^(p^(n - 1)) = 1(mod p^n) for all n = 1, 2, 3,... Would using the Binomial Thm help? What about applying the Chinese Remainder Thm? Click here to see answer by khwang(438)

 Question 4726: Show that 5n+3 and 7n+ 4 are relatively prime for all n Click here to see answer by khwang(438)

 Question 4871: Is 191 a prime number.How do i find out? Click here to see answer by rapaljer(4670)

 Question 5018: Which of the following numbers is a relative prime of 27? a.)24 b.)35 c.)45 d.)54 or e.)60? How did you come to this answer? Click here to see answer by rapaljer(4670)

 Question 5356: I need to solve : 1/2 + x/3 = 2x/3 - 1/4 Thanks for your help Click here to see answer by guapa(62)

 Question 5914: 1/2 + 4m = 3m -5/2 Clear the fractions first solve if neccesary Click here to see answer by Abbey(339)

 Question 5916: 1- 2/3y = 23 - 1/15y Clear the Fratctions Click here to see answer by longjonsilver(2297)

 Question 5915: a)1/2 + 4m = 3m - 5/2 Clear the Fractions first b)5/3 + 2/3x = 25/12 + 5/4x + 3/4 Click here to see answer by ichudov(499)

 Question 6222: Use the binomial theorem and mathematical induction to show the following. Let p be a prime. Then for any integer a, we have a^p =a (mod p). The "=" sign should be congruence. I need help, I have no idea what they want. Click here to see answer by khwang(438)

 Question 6657: What are the simple divisibility rules of first prime numbers? Click here to see answer by prabhjyot(164)

 Question 6746: what are the divisibility rules from 14 to 100? Click here to see answer by CharStar(110)

 Question 8010: I need to factor out, relative to the integers, all factors common to all terms. How do I do this?? Click here to see answer by glabow(165)

 Question 8604: What are the divisibilty rules to the numbers 13,14,15,16,17,18,19 and 20? Click here to see answer by mathsolver(3)
 Question 8604: What are the divisibilty rules to the numbers 13,14,15,16,17,18,19 and 20? Click here to see answer by rapaljer(4670)

 Question 5425: can you show me proof on the divisibility theories of both 9 and 11? Click here to see answer by mrduffner(11)

 Question 9134: I need help on this question. Find the probablilty of drawing a heart or a club from a standard 52 card deck Click here to see answer by longjonsilver(2297)
 Question 9134: I need help on this question. Find the probablilty of drawing a heart or a club from a standard 52 card deck Click here to see answer by rapaljer(4670)

 Question 9549: How do you find prime numbers up to 50? Click here to see answer by thecampusnerd(13)
 Question 9549: How do you find prime numbers up to 50? Click here to see answer by rapaljer(4670)

 Question 10288: I have created a method that tests divisibility by 7 and 13. It reduces an integer (doesn't matter its extension) to a two-digit number. Original number and reduced number divided by 7 will leave the same remainder. I would like to have your opinion about my method that is available at the site: www.7and13divisibility.com My best regards Silvio Moura Velho Click here to see answer by longjonsilver(2297)

 Question 10573: how can the square of a negative be a negative Click here to see answer by rapaljer(4670)

 Question 10808: is 1^5+2^5+3^5+.....+100^5 congruent to 0(mod 4). i know that all even numbers in this problem are divisible by 4. my problem lie in the odd numbers since some of them has a remainder 1 and some 3.is there a pattern for these odd numbers to know how many of them has a remainder 1 and how many has a remainder 3. Click here to see answer by khwang(438)

 Question 11090: is there a trick to finding a prime number Click here to see answer by Earlsdon(6294)

 Question 11353: what is the prime factorization of the number 1313 Click here to see answer by prabhjyot(164)

 Question 11823: Please help me solve this problem: Can you find a number less than 200 that is divisible by four different prime numbers? Why or Why not? Click here to see answer by longjonsilver(2297)

 Question 11896: write each number as a product of prime numbers a) 720 Click here to see answer by Earlsdon(6294)

 Question 12138: Hello- I need,(in a 6th grade defintion),help on DIVISIBILTY, and PRIME AND COMPOSITE NUMBERS!! It would help If you could explain the rules for: 2,5,10,and,3. and If possible type a short list of PRIME NUMBERS, and, COMPOSITE NUMBERS!! >.< My teacher didn't explain this in an eaasy way...LOL!! The worksheet is divided into four boxes, and in each box, I need to find all the numbers divisible by: 2,5,10,3. In each box I need to color in the numbers to create a picture!! THIS IS SO CUNFUSING!!!! NEED HELP ASAP!!!! Sincerely, -Anonymous Click here to see answer by rapaljer(4670)

 Question 12319: How do u prove this?...Show that 3 divides n^3-n for all positive integers n. And does 4 divide n^4-n for all positive intgers n? AND i need to use proof by induction i think, i get the first part but then get stuck at the end...please help Click here to see answer by khwang(438)