What is the Greatest Common Factor of 21960 and 21970?

Greatest common factor (GCF) of 21960 and 21970 is 10.

GCF(21960,21970) = 10

We will now calculate the prime factors of 21960 and 21970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21960 and 21970.

How to find the GCF of 21960 and 21970?

We will first find the prime factorization of 21960 and 21970. After we will calculate the factors of 21960 and 21970 and find the biggest common factor number .

Step-1: Prime Factorization of 21960

Prime factors of 21960 are 2, 3, 5, 61. Prime factorization of 21960 in exponential form is:

21960 = 2³ × 3² × 5¹ × 61¹

Step-2: Prime Factorization of 21970

Prime factors of 21970 are 2, 5, 13. Prime factorization of 21970 in exponential form is:

21970 = 2¹ × 5¹ × 13³

Step-3: Factors of 21960

List of positive integer factors of 21960 that divides 21960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980

Step-4: Factors of 21970

List of positive integer factors of 21970 that divides 21960 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 169, 338, 845, 1690, 2197, 4394, 10985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21960 and 21970. The biggest common factor number is the GCF number.
So the greatest common factor 21960 and 21970 is 10.

Also check out the Least Common Multiple of 21960 and 21970