Is (a,b) the GCD of a and b in a Divisibility Proof?

Thread starter wloger
Start date Mar 7, 2012
Tags

Divisibility Gcd Proof

In summary, Gcd (greatest common divisor) is the largest positive integer that divides both numbers without leaving a remainder. It is used in divisibility proofs by showing that the gcd of the two numbers is equal to the smaller number, which proves that the larger number is divisible by the smaller number. The process involves finding the gcd and if it is equal to the smaller number, the proof is valid. Any two numbers can be used as long as the gcd can be found and it is limited to integers. If the gcd cannot be found, it cannot be used in the proof.

Mar 7, 2012

wloger

Figured it out nvm

Last edited: Mar 7, 2012

Physics news on Phys.org

Mar 7, 2012

HallsofIvy

Science Advisor

Homework Helper

Are we to assume that (a,c) is the "greatest common denominator" of a and c?

Mar 7, 2012

wloger

yes (a,b) is the GCD of a and b

What is gcd?

Gcd stands for greatest common divisor. It is the largest positive integer that divides both numbers without leaving a remainder.

How is gcd used in divisibility proof?

Gcd is used to show that a number is divisible by another number. If the gcd of the two numbers is equal to the smaller number, then the larger number is divisible by the smaller number.

What is the process for using gcd in divisibility proof?

The process involves finding the gcd of the two numbers. Then, if the gcd is equal to the smaller number, it can be concluded that the larger number is divisible by the smaller number.