Question

. Let m be a positive integer, find the greatest common divisor of m and m+2

. Let m be a positive integer, find the greatest common divisor of m and m+2

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), or Highest Common Factor (HCF), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

Let m be a any positive integer.

For example , m=55 and, m+2 =57

factors of 55 are - 1,5 ,11, 55

factors of 57 are -1,3,19,57

Hence the greatest common divisor is 1.

Also,

There are many exceptions such as

For example,m=12 and, m+2=14

Factors of 12 are - 1,2,3,4,6,12

Factors of 14 are -1,2,7,14

Therefore, GCD is 2

There are exceptions but , 1 will be the common divisor for any positive integer (i.e. m and m+2)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let m be a positive integer, find the greatest common divisor of m and m +...
Let m be a positive integer, find the greatest common divisor of m and m + 2. *Please go step by step*
(Greatest Common Divisor) The greatest common divisor (GCD) of two integers is the largest integer that...
(Greatest Common Divisor) The greatest common divisor (GCD) of two integers is the largest integer that evenly divides each of the numbers. Write a JAVA program that returns the greatest common divisor of two integers.
ARM assembly Code The Euclidean algorithm is a way to find the greatest common divisor of...
ARM assembly Code The Euclidean algorithm is a way to find the greatest common divisor of two positive integers, a and b. First let me show the computations for a=210 and b=45. Divide 210 by 45, and get the result 4 with remainder 30, so 210=4·45+30. Divide 45 by 30, and get the result 1 with remainder 15, so 45=1·30+15. Divide 30 by 15, and get the result 2 with remainder 0, so 30=2·15+0. The greatest common divisor of 210...
Let m,n be any positive integers. Show that if m,n have no common prime divisor (i.e....
Let m,n be any positive integers. Show that if m,n have no common prime divisor (i.e. a divisor that is at the same time a prime number), then m+n and m have no common prime divisor. (Hint: try it indirectly)
Find the greatest common divisor of the given polynomials over the given field. Then write the...
Find the greatest common divisor of the given polynomials over the given field. Then write the greatest common divisor as a linear combination of the given polynomials. That is, given f(x) and g(x), find a(x) and b(x) so that d(x) = a(x)f(x) + b(x)g(x), where d(x) is the greatest common divisor of f(x) and g(x). (a) x^10 − x^7 − x^5 + x^3 + x^2 − 1 and x^8 − x^5 − x^3 + 1 over Q. (b) x^5 +...
Using the Euclidean Algorithm, find the Greatest Common Divisor and Bezout Coefficients of the following pair...
Using the Euclidean Algorithm, find the Greatest Common Divisor and Bezout Coefficients of the following pair of integers: (2002, 2339)
Two numbers are relatively prime if their greatest common divisor is 1. Show that if a...
Two numbers are relatively prime if their greatest common divisor is 1. Show that if a and b are relatively prime, then there exist integers m and n such that am+bn = 1. (proof by induction preferred)
16. Compute greatest common divisor of ?5 − 1 and ?3 + 2? − 3 in...
16. Compute greatest common divisor of ?5 − 1 and ?3 + 2? − 3 in modulus 13. 17. Check whether the polynomial is ?5 − 4?3 + 3?2 − ? + 2 is reducible or irreducible in modulus 3, 5 and 13
find greatest common divisor of x^5 + x^4 +1 and x^5+x+1, viewed as elements in the...
find greatest common divisor of x^5 + x^4 +1 and x^5+x+1, viewed as elements in the ring F2[x] of polynomials over the finite field F2 with 2 elements
Using the extended Euclidean algorithm, compute the greatest common divisor of 1819 and 3587.
Using the extended Euclidean algorithm, compute the greatest common divisor of 1819 and 3587.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT