What is the Greatest Common Factor of 10120 and 10140?

Greatest common factor (GCF) of 10120 and 10140 is 20.

GCF(10120,10140) = 20

We will now calculate the prime factors of 10120 and 10140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10120 and 10140.

How to find the GCF of 10120 and 10140?

We will first find the prime factorization of 10120 and 10140. After we will calculate the factors of 10120 and 10140 and find the biggest common factor number .

Step-1: Prime Factorization of 10120

Prime factors of 10120 are 2, 5, 11, 23. Prime factorization of 10120 in exponential form is:

10120 = 2³ × 5¹ × 11¹ × 23¹

Step-2: Prime Factorization of 10140

Prime factors of 10140 are 2, 3, 5, 13. Prime factorization of 10140 in exponential form is:

10140 = 2² × 3¹ × 5¹ × 13²

Step-3: Factors of 10120

List of positive integer factors of 10120 that divides 10120 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 23, 40, 44, 46, 55, 88, 92, 110, 115, 184, 220, 230, 253, 440, 460, 506, 920, 1012, 1265, 2024, 2530, 5060

Step-4: Factors of 10140

List of positive integer factors of 10140 that divides 10120 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 169, 195, 260, 338, 390, 507, 676, 780, 845, 1014, 1690, 2028, 2535, 3380, 5070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10120 and 10140. The biggest common factor number is the GCF number.
So the greatest common factor 10120 and 10140 is 20.

Also check out the Least Common Multiple of 10120 and 10140