What is the Greatest Common Factor of 31280 and 31300?

Greatest common factor (GCF) of 31280 and 31300 is 20.

GCF(31280,31300) = 20

We will now calculate the prime factors of 31280 and 31300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31280 and 31300.

How to find the GCF of 31280 and 31300?

We will first find the prime factorization of 31280 and 31300. After we will calculate the factors of 31280 and 31300 and find the biggest common factor number .

Step-1: Prime Factorization of 31280

Prime factors of 31280 are 2, 5, 17, 23. Prime factorization of 31280 in exponential form is:

31280 = 2⁴ × 5¹ × 17¹ × 23¹

Step-2: Prime Factorization of 31300

Prime factors of 31300 are 2, 5, 313. Prime factorization of 31300 in exponential form is:

31300 = 2² × 5² × 313¹

Step-3: Factors of 31280

List of positive integer factors of 31280 that divides 31280 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 23, 34, 40, 46, 68, 80, 85, 92, 115, 136, 170, 184, 230, 272, 340, 368, 391, 460, 680, 782, 920, 1360, 1564, 1840, 1955, 3128, 3910, 6256, 7820, 15640

Step-4: Factors of 31300

List of positive integer factors of 31300 that divides 31280 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 313, 626, 1252, 1565, 3130, 6260, 7825, 15650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31280 and 31300. The biggest common factor number is the GCF number.
So the greatest common factor 31280 and 31300 is 20.

Also check out the Least Common Multiple of 31280 and 31300