QuestionFind the GCD of 99 and 66. The GCD of 99 and 66 is $$.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the greatest common divisor (GCD) of99 and66. . The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

STEP 2

We will use the Euclidean algorithm to find the GCD of99 and66. The Euclidean algorithm is a way to find the greatest common divisor of two numbers based on the principle that the greatest common divisor of two numbers also divides their difference.
The Euclidean algorithm can be written as follows $gcd(a, b) = gcd(b, a \mod b)$

STEP 3

Let's start by applying the Euclidean algorithm to our numbers,99 and66.
$gcd(99,66) = gcd(66,99 \mod66)$

STEP 4

Calculate the modulus operation.
$99 \mod66 =33$ So, the equation becomes $gcd(99,66) = gcd(66,33)$

STEP 5

Repeat the process with the new pair of numbers.
$gcd(66,33) = gcd(33,66 \mod33)$

STEP 6

Calculate the modulus operation.
$66 \mod33 =0$ So, the equation becomes $gcd(66,33) = gcd(33,0)$

STEP 7

According to the Euclidean algorithm, when one of the numbers becomes0, the other number is the greatest common divisor. So, in this case, the GCD of99 and66 is33.
The greatest common divisor of99 and66 is33.

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