What is the Greatest Common Factor of 27960 and 27970?

Greatest common factor (GCF) of 27960 and 27970 is 10.

GCF(27960,27970) = 10

We will now calculate the prime factors of 27960 and 27970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27960 and 27970.

How to find the GCF of 27960 and 27970?

We will first find the prime factorization of 27960 and 27970. After we will calculate the factors of 27960 and 27970 and find the biggest common factor number .

Step-1: Prime Factorization of 27960

Prime factors of 27960 are 2, 3, 5, 233. Prime factorization of 27960 in exponential form is:

27960 = 2³ × 3¹ × 5¹ × 233¹

Step-2: Prime Factorization of 27970

Prime factors of 27970 are 2, 5, 2797. Prime factorization of 27970 in exponential form is:

27970 = 2¹ × 5¹ × 2797¹

Step-3: Factors of 27960

List of positive integer factors of 27960 that divides 27960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 233, 466, 699, 932, 1165, 1398, 1864, 2330, 2796, 3495, 4660, 5592, 6990, 9320, 13980

Step-4: Factors of 27970

List of positive integer factors of 27970 that divides 27960 without a remainder.

1, 2, 5, 10, 2797, 5594, 13985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27960 and 27970. The biggest common factor number is the GCF number.
So the greatest common factor 27960 and 27970 is 10.

Also check out the Least Common Multiple of 27960 and 27970