What is the Greatest Common Factor of 27768 and 27776?

Greatest common factor (GCF) of 27768 and 27776 is 8.

GCF(27768,27776) = 8

We will now calculate the prime factors of 27768 and 27776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27768 and 27776.

How to find the GCF of 27768 and 27776?

We will first find the prime factorization of 27768 and 27776. After we will calculate the factors of 27768 and 27776 and find the biggest common factor number .

Step-1: Prime Factorization of 27768

Prime factors of 27768 are 2, 3, 13, 89. Prime factorization of 27768 in exponential form is:

27768 = 2³ × 3¹ × 13¹ × 89¹

Step-2: Prime Factorization of 27776

Prime factors of 27776 are 2, 7, 31. Prime factorization of 27776 in exponential form is:

27776 = 2⁷ × 7¹ × 31¹

Step-3: Factors of 27768

List of positive integer factors of 27768 that divides 27768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 89, 104, 156, 178, 267, 312, 356, 534, 712, 1068, 1157, 2136, 2314, 3471, 4628, 6942, 9256, 13884

Step-4: Factors of 27776

List of positive integer factors of 27776 that divides 27768 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 112, 124, 128, 217, 224, 248, 434, 448, 496, 868, 896, 992, 1736, 1984, 3472, 3968, 6944, 13888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27768 and 27776. The biggest common factor number is the GCF number.
So the greatest common factor 27768 and 27776 is 8.

Also check out the Least Common Multiple of 27768 and 27776