What is the Greatest Common Factor of 65000 and 65008?

Greatest common factor (GCF) of 65000 and 65008 is 8.

GCF(65000,65008) = 8

We will now calculate the prime factors of 65000 and 65008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65000 and 65008.

How to find the GCF of 65000 and 65008?

We will first find the prime factorization of 65000 and 65008. After we will calculate the factors of 65000 and 65008 and find the biggest common factor number .

Step-1: Prime Factorization of 65000

Prime factors of 65000 are 2, 5, 13. Prime factorization of 65000 in exponential form is:

65000 = 2³ × 5⁴ × 13¹

Step-2: Prime Factorization of 65008

Prime factors of 65008 are 2, 17, 239. Prime factorization of 65008 in exponential form is:

65008 = 2⁴ × 17¹ × 239¹

Step-3: Factors of 65000

List of positive integer factors of 65000 that divides 65000 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 125, 130, 200, 250, 260, 325, 500, 520, 625, 650, 1000, 1250, 1300, 1625, 2500, 2600, 3250, 5000, 6500, 8125, 13000, 16250, 32500

Step-4: Factors of 65008

List of positive integer factors of 65008 that divides 65000 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 239, 272, 478, 956, 1912, 3824, 4063, 8126, 16252, 32504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65000 and 65008. The biggest common factor number is the GCF number.
So the greatest common factor 65000 and 65008 is 8.

Also check out the Least Common Multiple of 65000 and 65008