What is the Greatest Common Factor of 20961 and 20976?

Greatest common factor (GCF) of 20961 and 20976 is 3.

GCF(20961,20976) = 3

We will now calculate the prime factors of 20961 and 20976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20961 and 20976.

How to find the GCF of 20961 and 20976?

We will first find the prime factorization of 20961 and 20976. After we will calculate the factors of 20961 and 20976 and find the biggest common factor number .

Step-1: Prime Factorization of 20961

Prime factors of 20961 are 3, 17, 137. Prime factorization of 20961 in exponential form is:

20961 = 3² × 17¹ × 137¹

Step-2: Prime Factorization of 20976

Prime factors of 20976 are 2, 3, 19, 23. Prime factorization of 20976 in exponential form is:

20976 = 2⁴ × 3¹ × 19¹ × 23¹

Step-3: Factors of 20961

List of positive integer factors of 20961 that divides 20961 without a remainder.

1, 3, 9, 17, 51, 137, 153, 411, 1233, 2329, 6987

Step-4: Factors of 20976

List of positive integer factors of 20976 that divides 20961 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 23, 24, 38, 46, 48, 57, 69, 76, 92, 114, 138, 152, 184, 228, 276, 304, 368, 437, 456, 552, 874, 912, 1104, 1311, 1748, 2622, 3496, 5244, 6992, 10488

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20961 and 20976. The biggest common factor number is the GCF number.
So the greatest common factor 20961 and 20976 is 3.

Also check out the Least Common Multiple of 20961 and 20976