What is the Greatest Common Factor of 10140 and 10150?

Greatest common factor (GCF) of 10140 and 10150 is 10.

GCF(10140,10150) = 10

We will now calculate the prime factors of 10140 and 10150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10140 and 10150.

How to find the GCF of 10140 and 10150?

We will first find the prime factorization of 10140 and 10150. After we will calculate the factors of 10140 and 10150 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 10150

Prime factors of 10150 are 2, 5, 7, 29. Prime factorization of 10150 in exponential form is:

10150 = 2¹ × 5² × 7¹ × 29¹

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 10150

List of positive integer factors of 10150 that divides 10140 without a remainder.

1, 2, 5, 7, 10, 14, 25, 29, 35, 50, 58, 70, 145, 175, 203, 290, 350, 406, 725, 1015, 1450, 2030, 5075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10140 and 10150. The biggest common factor number is the GCF number.
So the greatest common factor 10140 and 10150 is 10.

Also check out the Least Common Multiple of 10140 and 10150