What is the Greatest Common Factor of 31120 and 31140?

Greatest common factor (GCF) of 31120 and 31140 is 20.

GCF(31120,31140) = 20

We will now calculate the prime factors of 31120 and 31140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31120 and 31140.

How to find the GCF of 31120 and 31140?

We will first find the prime factorization of 31120 and 31140. After we will calculate the factors of 31120 and 31140 and find the biggest common factor number .

Step-1: Prime Factorization of 31120

Prime factors of 31120 are 2, 5, 389. Prime factorization of 31120 in exponential form is:

31120 = 2⁴ × 5¹ × 389¹

Step-2: Prime Factorization of 31140

Prime factors of 31140 are 2, 3, 5, 173. Prime factorization of 31140 in exponential form is:

31140 = 2² × 3² × 5¹ × 173¹

Step-3: Factors of 31120

List of positive integer factors of 31120 that divides 31120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 389, 778, 1556, 1945, 3112, 3890, 6224, 7780, 15560

Step-4: Factors of 31140

List of positive integer factors of 31140 that divides 31120 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 173, 180, 346, 519, 692, 865, 1038, 1557, 1730, 2076, 2595, 3114, 3460, 5190, 6228, 7785, 10380, 15570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31120 and 31140. The biggest common factor number is the GCF number.
So the greatest common factor 31120 and 31140 is 20.

Also check out the Least Common Multiple of 31120 and 31140