What is the Greatest Common Factor of 35140 and 35160?

Greatest common factor (GCF) of 35140 and 35160 is 20.

GCF(35140,35160) = 20

We will now calculate the prime factors of 35140 and 35160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35140 and 35160.

How to find the GCF of 35140 and 35160?

We will first find the prime factorization of 35140 and 35160. After we will calculate the factors of 35140 and 35160 and find the biggest common factor number .

Step-1: Prime Factorization of 35140

Prime factors of 35140 are 2, 5, 7, 251. Prime factorization of 35140 in exponential form is:

35140 = 2² × 5¹ × 7¹ × 251¹

Step-2: Prime Factorization of 35160

Prime factors of 35160 are 2, 3, 5, 293. Prime factorization of 35160 in exponential form is:

35160 = 2³ × 3¹ × 5¹ × 293¹

Step-3: Factors of 35140

List of positive integer factors of 35140 that divides 35140 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 251, 502, 1004, 1255, 1757, 2510, 3514, 5020, 7028, 8785, 17570

Step-4: Factors of 35160

List of positive integer factors of 35160 that divides 35140 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 293, 586, 879, 1172, 1465, 1758, 2344, 2930, 3516, 4395, 5860, 7032, 8790, 11720, 17580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35140 and 35160. The biggest common factor number is the GCF number.
So the greatest common factor 35140 and 35160 is 20.

Also check out the Least Common Multiple of 35140 and 35160