What is the Greatest Common Factor of 45000 and 45008?

Greatest common factor (GCF) of 45000 and 45008 is 8.

GCF(45000,45008) = 8

We will now calculate the prime factors of 45000 and 45008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45000 and 45008.

How to find the GCF of 45000 and 45008?

We will first find the prime factorization of 45000 and 45008. After we will calculate the factors of 45000 and 45008 and find the biggest common factor number .

Step-1: Prime Factorization of 45000

Prime factors of 45000 are 2, 3, 5. Prime factorization of 45000 in exponential form is:

45000 = 2³ × 3² × 5⁴

Step-2: Prime Factorization of 45008

Prime factors of 45008 are 2, 29, 97. Prime factorization of 45008 in exponential form is:

45008 = 2⁴ × 29¹ × 97¹

Step-3: Factors of 45000

List of positive integer factors of 45000 that divides 45000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 625, 750, 900, 1000, 1125, 1250, 1500, 1800, 1875, 2250, 2500, 3000, 3750, 4500, 5000, 5625, 7500, 9000, 11250, 15000, 22500

Step-4: Factors of 45008

List of positive integer factors of 45008 that divides 45000 without a remainder.

1, 2, 4, 8, 16, 29, 58, 97, 116, 194, 232, 388, 464, 776, 1552, 2813, 5626, 11252, 22504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45000 and 45008. The biggest common factor number is the GCF number.
So the greatest common factor 45000 and 45008 is 8.

Also check out the Least Common Multiple of 45000 and 45008