What is the Greatest Common Factor of 25120 and 25140?

Greatest common factor (GCF) of 25120 and 25140 is 20.

GCF(25120,25140) = 20

We will now calculate the prime factors of 25120 and 25140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25120 and 25140.

How to find the GCF of 25120 and 25140?

We will first find the prime factorization of 25120 and 25140. After we will calculate the factors of 25120 and 25140 and find the biggest common factor number .

Step-1: Prime Factorization of 25120

Prime factors of 25120 are 2, 5, 157. Prime factorization of 25120 in exponential form is:

25120 = 2⁵ × 5¹ × 157¹

Step-2: Prime Factorization of 25140

Prime factors of 25140 are 2, 3, 5, 419. Prime factorization of 25140 in exponential form is:

25140 = 2² × 3¹ × 5¹ × 419¹

Step-3: Factors of 25120

List of positive integer factors of 25120 that divides 25120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 157, 160, 314, 628, 785, 1256, 1570, 2512, 3140, 5024, 6280, 12560

Step-4: Factors of 25140

List of positive integer factors of 25140 that divides 25120 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 419, 838, 1257, 1676, 2095, 2514, 4190, 5028, 6285, 8380, 12570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25120 and 25140. The biggest common factor number is the GCF number.
So the greatest common factor 25120 and 25140 is 20.

Also check out the Least Common Multiple of 25120 and 25140