What is the Greatest Common Factor of 67140 and 67160?

Greatest common factor (GCF) of 67140 and 67160 is 20.

GCF(67140,67160) = 20

We will now calculate the prime factors of 67140 and 67160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67140 and 67160.

How to find the GCF of 67140 and 67160?

We will first find the prime factorization of 67140 and 67160. After we will calculate the factors of 67140 and 67160 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67160

Prime factors of 67160 are 2, 5, 23, 73. Prime factorization of 67160 in exponential form is:

67160 = 2³ × 5¹ × 23¹ × 73¹

Step-3: Factors of 67140

List of positive integer factors of 67140 that divides 67140 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

Step-4: Factors of 67160

List of positive integer factors of 67160 that divides 67140 without a remainder.

1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 73, 92, 115, 146, 184, 230, 292, 365, 460, 584, 730, 920, 1460, 1679, 2920, 3358, 6716, 8395, 13432, 16790, 33580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67140 and 67160. The biggest common factor number is the GCF number.
So the greatest common factor 67140 and 67160 is 20.

Also check out the Least Common Multiple of 67140 and 67160