What is the Greatest Common Factor of 71960 and 71974?

Greatest common factor (GCF) of 71960 and 71974 is 14.

GCF(71960,71974) = 14

We will now calculate the prime factors of 71960 and 71974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71960 and 71974.

How to find the GCF of 71960 and 71974?

We will first find the prime factorization of 71960 and 71974. After we will calculate the factors of 71960 and 71974 and find the biggest common factor number .

Step-1: Prime Factorization of 71960

Prime factors of 71960 are 2, 5, 7, 257. Prime factorization of 71960 in exponential form is:

71960 = 2³ × 5¹ × 7¹ × 257¹

Step-2: 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-3: Factors of 71960

List of positive integer factors of 71960 that divides 71960 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 257, 280, 514, 1028, 1285, 1799, 2056, 2570, 3598, 5140, 7196, 8995, 10280, 14392, 17990, 35980

Step-4: Factors of 71974

List of positive integer factors of 71974 that divides 71960 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71960 and 71974. The biggest common factor number is the GCF number.
So the greatest common factor 71960 and 71974 is 14.

Also check out the Least Common Multiple of 71960 and 71974