What is the Greatest Common Factor of 35000 and 35007?

Greatest common factor (GCF) of 35000 and 35007 is 7.

GCF(35000,35007) = 7

We will now calculate the prime factors of 35000 and 35007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35000 and 35007.

How to find the GCF of 35000 and 35007?

We will first find the prime factorization of 35000 and 35007. After we will calculate the factors of 35000 and 35007 and find the biggest common factor number .

Step-1: Prime Factorization of 35000

Prime factors of 35000 are 2, 5, 7. Prime factorization of 35000 in exponential form is:

35000 = 2³ × 5⁴ × 7¹

Step-2: Prime Factorization of 35007

Prime factors of 35007 are 3, 7, 1667. Prime factorization of 35007 in exponential form is:

35007 = 3¹ × 7¹ × 1667¹

Step-3: Factors of 35000

List of positive integer factors of 35000 that divides 35000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 625, 700, 875, 1000, 1250, 1400, 1750, 2500, 3500, 4375, 5000, 7000, 8750, 17500

Step-4: Factors of 35007

List of positive integer factors of 35007 that divides 35000 without a remainder.

1, 3, 7, 21, 1667, 5001, 11669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35000 and 35007. The biggest common factor number is the GCF number.
So the greatest common factor 35000 and 35007 is 7.

Also check out the Least Common Multiple of 35000 and 35007