What is the Greatest Common Factor of 10140 and 10146?

Greatest common factor (GCF) of 10140 and 10146 is 6.

GCF(10140,10146) = 6

We will now calculate the prime factors of 10140 and 10146, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10140 and 10146.

How to find the GCF of 10140 and 10146?

We will first find the prime factorization of 10140 and 10146. After we will calculate the factors of 10140 and 10146 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 10146

Prime factors of 10146 are 2, 3, 19, 89. Prime factorization of 10146 in exponential form is:

10146 = 2¹ × 3¹ × 19¹ × 89¹

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 10146

List of positive integer factors of 10146 that divides 10140 without a remainder.

1, 2, 3, 6, 19, 38, 57, 89, 114, 178, 267, 534, 1691, 3382, 5073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10140 and 10146. The biggest common factor number is the GCF number.
So the greatest common factor 10140 and 10146 is 6.

Also check out the Least Common Multiple of 10140 and 10146