What is the greatest common divisor of 9 and 6?

What is the greatest common divisor of 9 and 6?

• A. 9
• B. 6
• C. 1
• D. 3

Answer: (D)

The greatest common divisor is the largest number that can divide both numbers evenly. For 9 and 6, the divisors are: 9 is divisible by 1, 3, and 9; 6 is divisible by 1, 2, 3, and 6. The common divisors are 1 and 3, and the largest of these is 3. So the greatest common divisor is 3. This also explains why neither 9 nor 6 can be the gcd, since one doesn’t evenly divide the other. Knowing the gcd helps with simplifying fractions, like turning 9/6 into 3/2 by dividing numerator and denominator by 3.

The greatest common divisor is the largest number that can divide both numbers evenly. For 9 and 6, the divisors are: 9 is divisible by 1, 3, and 9; 6 is divisible by 1, 2, 3, and 6. The common divisors are 1 and 3, and the largest of these is 3. So the greatest common divisor is 3. This also explains why neither 9 nor 6 can be the gcd, since one doesn’t evenly divide the other. Knowing the gcd helps with simplifying fractions, like turning 9/6 into 3/2 by dividing numerator and denominator by 3.