What is the Greatest Common Factor of 10972 and 10985?

Greatest common factor (GCF) of 10972 and 10985 is 13.

GCF(10972,10985) = 13

We will now calculate the prime factors of 10972 and 10985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10972 and 10985.

How to find the GCF of 10972 and 10985?

We will first find the prime factorization of 10972 and 10985. After we will calculate the factors of 10972 and 10985 and find the biggest common factor number .

Step-1: Prime Factorization of 10972

Prime factors of 10972 are 2, 13, 211. Prime factorization of 10972 in exponential form is:

10972 = 2² × 13¹ × 211¹

Step-2: Prime Factorization of 10985

Prime factors of 10985 are 5, 13. Prime factorization of 10985 in exponential form is:

10985 = 5¹ × 13³

Step-3: Factors of 10972

List of positive integer factors of 10972 that divides 10972 without a remainder.

1, 2, 4, 13, 26, 52, 211, 422, 844, 2743, 5486

Step-4: Factors of 10985

List of positive integer factors of 10985 that divides 10972 without a remainder.

1, 5, 13, 65, 169, 845, 2197

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10972 and 10985. The biggest common factor number is the GCF number.
So the greatest common factor 10972 and 10985 is 13.

Also check out the Least Common Multiple of 10972 and 10985