What is the Greatest Common Factor of 4140 and 4160?

Greatest common factor (GCF) of 4140 and 4160 is 20.

GCF(4140,4160) = 20

We will now calculate the prime factors of 4140 and 4160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4140 and 4160.

How to find the GCF of 4140 and 4160?

We will first find the prime factorization of 4140 and 4160. After we will calculate the factors of 4140 and 4160 and find the biggest common factor number .

Step-1: Prime Factorization of 4140

Prime factors of 4140 are 2, 3, 5, 23. Prime factorization of 4140 in exponential form is:

4140 = 2² × 3² × 5¹ × 23¹

Step-2: Prime Factorization of 4160

Prime factors of 4160 are 2, 5, 13. Prime factorization of 4160 in exponential form is:

4160 = 2⁶ × 5¹ × 13¹

Step-3: Factors of 4140

List of positive integer factors of 4140 that divides 4140 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45, 46, 60, 69, 90, 92, 115, 138, 180, 207, 230, 276, 345, 414, 460, 690, 828, 1035, 1380, 2070

Step-4: Factors of 4160

List of positive integer factors of 4160 that divides 4140 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 64, 65, 80, 104, 130, 160, 208, 260, 320, 416, 520, 832, 1040, 2080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4140 and 4160. The biggest common factor number is the GCF number.
So the greatest common factor 4140 and 4160 is 20.

Also check out the Least Common Multiple of 4140 and 4160