What is the Greatest Common Factor of 71000 and 71008?

Greatest common factor (GCF) of 71000 and 71008 is 8.

GCF(71000,71008) = 8

We will now calculate the prime factors of 71000 and 71008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71000 and 71008.

How to find the GCF of 71000 and 71008?

We will first find the prime factorization of 71000 and 71008. After we will calculate the factors of 71000 and 71008 and find the biggest common factor number .

Step-1: Prime Factorization of 71000

Prime factors of 71000 are 2, 5, 71. Prime factorization of 71000 in exponential form is:

71000 = 2³ × 5³ × 71¹

Step-2: Prime Factorization of 71008

Prime factors of 71008 are 2, 7, 317. Prime factorization of 71008 in exponential form is:

71008 = 2⁵ × 7¹ × 317¹

Step-3: Factors of 71000

List of positive integer factors of 71000 that divides 71000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 71, 100, 125, 142, 200, 250, 284, 355, 500, 568, 710, 1000, 1420, 1775, 2840, 3550, 7100, 8875, 14200, 17750, 35500

Step-4: Factors of 71008

List of positive integer factors of 71008 that divides 71000 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 317, 634, 1268, 2219, 2536, 4438, 5072, 8876, 10144, 17752, 35504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71000 and 71008. The biggest common factor number is the GCF number.
So the greatest common factor 71000 and 71008 is 8.

Also check out the Least Common Multiple of 71000 and 71008