What is the Greatest Common Factor of 10140 and 10160?

Greatest common factor (GCF) of 10140 and 10160 is 20.

GCF(10140,10160) = 20

We will now calculate the prime factors of 10140 and 10160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10140 and 10160.

How to find the GCF of 10140 and 10160?

We will first find the prime factorization of 10140 and 10160. After we will calculate the factors of 10140 and 10160 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10160

Prime factors of 10160 are 2, 5, 127. Prime factorization of 10160 in exponential form is:

10160 = 2⁴ × 5¹ × 127¹

Step-3: Factors of 10140

List of positive integer factors of 10140 that divides 10140 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

Step-4: Factors of 10160

List of positive integer factors of 10160 that divides 10140 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 127, 254, 508, 635, 1016, 1270, 2032, 2540, 5080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10140 and 10160. The biggest common factor number is the GCF number.
So the greatest common factor 10140 and 10160 is 20.

Also check out the Least Common Multiple of 10140 and 10160