What is the Greatest Common Factor of 67914 and 67920?

Greatest common factor (GCF) of 67914 and 67920 is 6.

GCF(67914,67920) = 6

We will now calculate the prime factors of 67914 and 67920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67914 and 67920.

How to find the GCF of 67914 and 67920?

We will first find the prime factorization of 67914 and 67920. After we will calculate the factors of 67914 and 67920 and find the biggest common factor number .

Step-1: Prime Factorization of 67914

Prime factors of 67914 are 2, 3, 7, 11. Prime factorization of 67914 in exponential form is:

67914 = 2¹ × 3² × 7³ × 11¹

Step-2: Prime Factorization of 67920

Prime factors of 67920 are 2, 3, 5, 283. Prime factorization of 67920 in exponential form is:

67920 = 2⁴ × 3¹ × 5¹ × 283¹

Step-3: Factors of 67914

List of positive integer factors of 67914 that divides 67914 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 49, 63, 66, 77, 98, 99, 126, 147, 154, 198, 231, 294, 343, 441, 462, 539, 686, 693, 882, 1029, 1078, 1386, 1617, 2058, 3087, 3234, 3773, 4851, 6174, 7546, 9702, 11319, 22638, 33957

Step-4: Factors of 67920

List of positive integer factors of 67920 that divides 67914 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 283, 566, 849, 1132, 1415, 1698, 2264, 2830, 3396, 4245, 4528, 5660, 6792, 8490, 11320, 13584, 16980, 22640, 33960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67914 and 67920. The biggest common factor number is the GCF number.
So the greatest common factor 67914 and 67920 is 6.

Also check out the Least Common Multiple of 67914 and 67920