What is the Greatest Common Factor of 71974 and 71988?

Greatest common factor (GCF) of 71974 and 71988 is 14.

GCF(71974,71988) = 14

We will now calculate the prime factors of 71974 and 71988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71974 and 71988.

How to find the GCF of 71974 and 71988?

We will first find the prime factorization of 71974 and 71988. After we will calculate the factors of 71974 and 71988 and find the biggest common factor number .

Step-1: Prime Factorization of 71974

Prime factors of 71974 are 2, 7, 53, 97. Prime factorization of 71974 in exponential form is:

71974 = 2¹ × 7¹ × 53¹ × 97¹

Step-2: Prime Factorization of 71988

Prime factors of 71988 are 2, 3, 7, 857. Prime factorization of 71988 in exponential form is:

71988 = 2² × 3¹ × 7¹ × 857¹

Step-3: Factors of 71974

List of positive integer factors of 71974 that divides 71974 without a remainder.

1, 2, 7, 14, 53, 97, 106, 194, 371, 679, 742, 1358, 5141, 10282, 35987

Step-4: Factors of 71988

List of positive integer factors of 71988 that divides 71974 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 857, 1714, 2571, 3428, 5142, 5999, 10284, 11998, 17997, 23996, 35994

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71974 and 71988. The biggest common factor number is the GCF number.
So the greatest common factor 71974 and 71988 is 14.

Also check out the Least Common Multiple of 71974 and 71988