What is the Greatest Common Factor of 27874 and 27888?

Greatest common factor (GCF) of 27874 and 27888 is 14.

GCF(27874,27888) = 14

We will now calculate the prime factors of 27874 and 27888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27874 and 27888.

How to find the GCF of 27874 and 27888?

We will first find the prime factorization of 27874 and 27888. After we will calculate the factors of 27874 and 27888 and find the biggest common factor number .

Step-1: Prime Factorization of 27874

Prime factors of 27874 are 2, 7, 11, 181. Prime factorization of 27874 in exponential form is:

27874 = 2¹ × 7¹ × 11¹ × 181¹

Step-2: Prime Factorization of 27888

Prime factors of 27888 are 2, 3, 7, 83. Prime factorization of 27888 in exponential form is:

27888 = 2⁴ × 3¹ × 7¹ × 83¹

Step-3: Factors of 27874

List of positive integer factors of 27874 that divides 27874 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 181, 362, 1267, 1991, 2534, 3982, 13937

Step-4: Factors of 27888

List of positive integer factors of 27888 that divides 27874 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 83, 84, 112, 166, 168, 249, 332, 336, 498, 581, 664, 996, 1162, 1328, 1743, 1992, 2324, 3486, 3984, 4648, 6972, 9296, 13944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27874 and 27888. The biggest common factor number is the GCF number.
So the greatest common factor 27874 and 27888 is 14.

Also check out the Least Common Multiple of 27874 and 27888