What is the Greatest Common Factor of 97971 and 97988?

Greatest common factor (GCF) of 97971 and 97988 is 17.

GCF(97971,97988) = 17

We will now calculate the prime factors of 97971 and 97988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 97971 and 97988.

How to find the GCF of 97971 and 97988?

We will first find the prime factorization of 97971 and 97988. After we will calculate the factors of 97971 and 97988 and find the biggest common factor number .

Step-1: Prime Factorization of 97971

Prime factors of 97971 are 3, 17, 113. Prime factorization of 97971 in exponential form is:

97971 = 3¹ × 17² × 113¹

Step-2: Prime Factorization of 97988

Prime factors of 97988 are 2, 11, 17, 131. Prime factorization of 97988 in exponential form is:

97988 = 2² × 11¹ × 17¹ × 131¹

Step-3: Factors of 97971

List of positive integer factors of 97971 that divides 97971 without a remainder.

1, 3, 17, 51, 113, 289, 339, 867, 1921, 5763, 32657

Step-4: Factors of 97988

List of positive integer factors of 97988 that divides 97971 without a remainder.

1, 2, 4, 11, 17, 22, 34, 44, 68, 131, 187, 262, 374, 524, 748, 1441, 2227, 2882, 4454, 5764, 8908, 24497, 48994

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 97971 and 97988. The biggest common factor number is the GCF number.
So the greatest common factor 97971 and 97988 is 17.

Also check out the Least Common Multiple of 97971 and 97988