What is the Greatest Common Factor of 26970 and 26980?

Greatest common factor (GCF) of 26970 and 26980 is 10.

GCF(26970,26980) = 10

We will now calculate the prime factors of 26970 and 26980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26970 and 26980.

How to find the GCF of 26970 and 26980?

We will first find the prime factorization of 26970 and 26980. After we will calculate the factors of 26970 and 26980 and find the biggest common factor number .

Step-1: Prime Factorization of 26970

Prime factors of 26970 are 2, 3, 5, 29, 31. Prime factorization of 26970 in exponential form is:

26970 = 2¹ × 3¹ × 5¹ × 29¹ × 31¹

Step-2: Prime Factorization of 26980

Prime factors of 26980 are 2, 5, 19, 71. Prime factorization of 26980 in exponential form is:

26980 = 2² × 5¹ × 19¹ × 71¹

Step-3: Factors of 26970

List of positive integer factors of 26970 that divides 26970 without a remainder.

1, 2, 3, 5, 6, 10, 15, 29, 30, 31, 58, 62, 87, 93, 145, 155, 174, 186, 290, 310, 435, 465, 870, 899, 930, 1798, 2697, 4495, 5394, 8990, 13485

Step-4: Factors of 26980

List of positive integer factors of 26980 that divides 26970 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 71, 76, 95, 142, 190, 284, 355, 380, 710, 1349, 1420, 2698, 5396, 6745, 13490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26970 and 26980. The biggest common factor number is the GCF number.
So the greatest common factor 26970 and 26980 is 10.

Also check out the Least Common Multiple of 26970 and 26980