What is the Greatest Common Factor of 31440 and 31460?

Greatest common factor (GCF) of 31440 and 31460 is 20.

GCF(31440,31460) = 20

We will now calculate the prime factors of 31440 and 31460, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31440 and 31460.

How to find the GCF of 31440 and 31460?

We will first find the prime factorization of 31440 and 31460. After we will calculate the factors of 31440 and 31460 and find the biggest common factor number .

Step-1: Prime Factorization of 31440

Prime factors of 31440 are 2, 3, 5, 131. Prime factorization of 31440 in exponential form is:

31440 = 2⁴ × 3¹ × 5¹ × 131¹

Step-2: Prime Factorization of 31460

Prime factors of 31460 are 2, 5, 11, 13. Prime factorization of 31460 in exponential form is:

31460 = 2² × 5¹ × 11² × 13¹

Step-3: Factors of 31440

List of positive integer factors of 31440 that divides 31440 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 131, 240, 262, 393, 524, 655, 786, 1048, 1310, 1572, 1965, 2096, 2620, 3144, 3930, 5240, 6288, 7860, 10480, 15720

Step-4: Factors of 31460

List of positive integer factors of 31460 that divides 31440 without a remainder.

1, 2, 4, 5, 10, 11, 13, 20, 22, 26, 44, 52, 55, 65, 110, 121, 130, 143, 220, 242, 260, 286, 484, 572, 605, 715, 1210, 1430, 1573, 2420, 2860, 3146, 6292, 7865, 15730

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31440 and 31460. The biggest common factor number is the GCF number.
So the greatest common factor 31440 and 31460 is 20.

Also check out the Least Common Multiple of 31440 and 31460