What is the Greatest Common Factor of 67120 and 67140?

Greatest common factor (GCF) of 67120 and 67140 is 20.

GCF(67120,67140) = 20

We will now calculate the prime factors of 67120 and 67140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67120 and 67140.

How to find the GCF of 67120 and 67140?

We will first find the prime factorization of 67120 and 67140. After we will calculate the factors of 67120 and 67140 and find the biggest common factor number .

Step-1: Prime Factorization of 67120

Prime factors of 67120 are 2, 5, 839. Prime factorization of 67120 in exponential form is:

67120 = 2⁴ × 5¹ × 839¹

Step-2: Prime Factorization of 67140

Prime factors of 67140 are 2, 3, 5, 373. Prime factorization of 67140 in exponential form is:

67140 = 2² × 3² × 5¹ × 373¹

Step-3: Factors of 67120

List of positive integer factors of 67120 that divides 67120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 839, 1678, 3356, 4195, 6712, 8390, 13424, 16780, 33560

Step-4: Factors of 67140

List of positive integer factors of 67140 that divides 67120 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 373, 746, 1119, 1492, 1865, 2238, 3357, 3730, 4476, 5595, 6714, 7460, 11190, 13428, 16785, 22380, 33570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67120 and 67140. The biggest common factor number is the GCF number.
So the greatest common factor 67120 and 67140 is 20.

Also check out the Least Common Multiple of 67120 and 67140