What is the Greatest Common Factor of 35120 and 35140?

Greatest common factor (GCF) of 35120 and 35140 is 20.

GCF(35120,35140) = 20

We will now calculate the prime factors of 35120 and 35140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35120 and 35140.

How to find the GCF of 35120 and 35140?

We will first find the prime factorization of 35120 and 35140. After we will calculate the factors of 35120 and 35140 and find the biggest common factor number .

Step-1: Prime Factorization of 35120

Prime factors of 35120 are 2, 5, 439. Prime factorization of 35120 in exponential form is:

35120 = 2⁴ × 5¹ × 439¹

Step-2: 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-3: Factors of 35120

List of positive integer factors of 35120 that divides 35120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 439, 878, 1756, 2195, 3512, 4390, 7024, 8780, 17560

Step-4: Factors of 35140

List of positive integer factors of 35140 that divides 35120 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35120 and 35140. The biggest common factor number is the GCF number.
So the greatest common factor 35120 and 35140 is 20.

Also check out the Least Common Multiple of 35120 and 35140