What is the Greatest Common Factor of 10960 and 10974?

Greatest common factor (GCF) of 10960 and 10974 is 2.

GCF(10960,10974) = 2

We will now calculate the prime factors of 10960 and 10974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10960 and 10974.

How to find the GCF of 10960 and 10974?

We will first find the prime factorization of 10960 and 10974. After we will calculate the factors of 10960 and 10974 and find the biggest common factor number .

Step-1: Prime Factorization of 10960

Prime factors of 10960 are 2, 5, 137. Prime factorization of 10960 in exponential form is:

10960 = 2⁴ × 5¹ × 137¹

Step-2: Prime Factorization of 10974

Prime factors of 10974 are 2, 3, 31, 59. Prime factorization of 10974 in exponential form is:

10974 = 2¹ × 3¹ × 31¹ × 59¹

Step-3: Factors of 10960

List of positive integer factors of 10960 that divides 10960 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 137, 274, 548, 685, 1096, 1370, 2192, 2740, 5480

Step-4: Factors of 10974

List of positive integer factors of 10974 that divides 10960 without a remainder.

1, 2, 3, 6, 31, 59, 62, 93, 118, 177, 186, 354, 1829, 3658, 5487

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10960 and 10974. The biggest common factor number is the GCF number.
So the greatest common factor 10960 and 10974 is 2.

Also check out the Least Common Multiple of 10960 and 10974