What is the Greatest Common Factor of 21996 and 22009?

Greatest common factor (GCF) of 21996 and 22009 is 13.

GCF(21996,22009) = 13

We will now calculate the prime factors of 21996 and 22009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21996 and 22009.

How to find the GCF of 21996 and 22009?

We will first find the prime factorization of 21996 and 22009. After we will calculate the factors of 21996 and 22009 and find the biggest common factor number .

Step-1: Prime Factorization of 21996

Prime factors of 21996 are 2, 3, 13, 47. Prime factorization of 21996 in exponential form is:

21996 = 2² × 3² × 13¹ × 47¹

Step-2: Prime Factorization of 22009

Prime factors of 22009 are 13, 1693. Prime factorization of 22009 in exponential form is:

22009 = 13¹ × 1693¹

Step-3: Factors of 21996

List of positive integer factors of 21996 that divides 21996 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 47, 52, 78, 94, 117, 141, 156, 188, 234, 282, 423, 468, 564, 611, 846, 1222, 1692, 1833, 2444, 3666, 5499, 7332, 10998

Step-4: Factors of 22009

List of positive integer factors of 22009 that divides 21996 without a remainder.

1, 13, 1693

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21996 and 22009. The biggest common factor number is the GCF number.
So the greatest common factor 21996 and 22009 is 13.

Also check out the Least Common Multiple of 21996 and 22009