What is the Greatest Common Factor of 25977 and 25984?

Greatest common factor (GCF) of 25977 and 25984 is 7.

GCF(25977,25984) = 7

We will now calculate the prime factors of 25977 and 25984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25977 and 25984.

How to find the GCF of 25977 and 25984?

We will first find the prime factorization of 25977 and 25984. After we will calculate the factors of 25977 and 25984 and find the biggest common factor number .

Step-1: Prime Factorization of 25977

Prime factors of 25977 are 3, 7, 1237. Prime factorization of 25977 in exponential form is:

25977 = 3¹ × 7¹ × 1237¹

Step-2: Prime Factorization of 25984

Prime factors of 25984 are 2, 7, 29. Prime factorization of 25984 in exponential form is:

25984 = 2⁷ × 7¹ × 29¹

Step-3: Factors of 25977

List of positive integer factors of 25977 that divides 25977 without a remainder.

1, 3, 7, 21, 1237, 3711, 8659

Step-4: Factors of 25984

List of positive integer factors of 25984 that divides 25977 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 29, 32, 56, 58, 64, 112, 116, 128, 203, 224, 232, 406, 448, 464, 812, 896, 928, 1624, 1856, 3248, 3712, 6496, 12992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25977 and 25984. The biggest common factor number is the GCF number.
So the greatest common factor 25977 and 25984 is 7.

Also check out the Least Common Multiple of 25977 and 25984