What is the Greatest Common Factor of 67776 and 67782?

Greatest common factor (GCF) of 67776 and 67782 is 6.

GCF(67776,67782) = 6

We will now calculate the prime factors of 67776 and 67782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67776 and 67782.

How to find the GCF of 67776 and 67782?

We will first find the prime factorization of 67776 and 67782. After we will calculate the factors of 67776 and 67782 and find the biggest common factor number .

Step-1: Prime Factorization of 67776

Prime factors of 67776 are 2, 3, 353. Prime factorization of 67776 in exponential form is:

67776 = 2⁶ × 3¹ × 353¹

Step-2: Prime Factorization of 67782

Prime factors of 67782 are 2, 3, 11, 13, 79. Prime factorization of 67782 in exponential form is:

67782 = 2¹ × 3¹ × 11¹ × 13¹ × 79¹

Step-3: Factors of 67776

List of positive integer factors of 67776 that divides 67776 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 353, 706, 1059, 1412, 2118, 2824, 4236, 5648, 8472, 11296, 16944, 22592, 33888

Step-4: Factors of 67782

List of positive integer factors of 67782 that divides 67776 without a remainder.

1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 79, 143, 158, 237, 286, 429, 474, 858, 869, 1027, 1738, 2054, 2607, 3081, 5214, 6162, 11297, 22594, 33891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67776 and 67782. The biggest common factor number is the GCF number.
So the greatest common factor 67776 and 67782 is 6.

Also check out the Least Common Multiple of 67776 and 67782