What is the Greatest Common Factor of 9709 and 9714?

Greatest common factor (GCF) of 9709 and 9714 is 1.

GCF(9709,9714) = 1

We will now calculate the prime factors of 9709 and 9714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9709 and 9714.

How to find the GCF of 9709 and 9714?

We will first find the prime factorization of 9709 and 9714. After we will calculate the factors of 9709 and 9714 and find the biggest common factor number .

Step-1: Prime Factorization of 9709

Prime factors of 9709 are 7, 19, 73. Prime factorization of 9709 in exponential form is:

9709 = 7¹ × 19¹ × 73¹

Step-2: Prime Factorization of 9714

Prime factors of 9714 are 2, 3, 1619. Prime factorization of 9714 in exponential form is:

9714 = 2¹ × 3¹ × 1619¹

Step-3: Factors of 9709

List of positive integer factors of 9709 that divides 9709 without a remainder.

1, 7, 19, 73, 133, 511, 1387

Step-4: Factors of 9714

List of positive integer factors of 9714 that divides 9709 without a remainder.

1, 2, 3, 6, 1619, 3238, 4857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9709 and 9714. The biggest common factor number is the GCF number.
So the greatest common factor 9709 and 9714 is 1.

Also check out the Least Common Multiple of 9709 and 9714