What is the Greatest Common Factor of 35000 and 35014?

Greatest common factor (GCF) of 35000 and 35014 is 14.

GCF(35000,35014) = 14

We will now calculate the prime factors of 35000 and 35014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35000 and 35014.

How to find the GCF of 35000 and 35014?

We will first find the prime factorization of 35000 and 35014. After we will calculate the factors of 35000 and 35014 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 35014

Prime factors of 35014 are 2, 7, 41, 61. Prime factorization of 35014 in exponential form is:

35014 = 2¹ × 7¹ × 41¹ × 61¹

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 35014

List of positive integer factors of 35014 that divides 35000 without a remainder.

1, 2, 7, 14, 41, 61, 82, 122, 287, 427, 574, 854, 2501, 5002, 17507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35000 and 35014. The biggest common factor number is the GCF number.
So the greatest common factor 35000 and 35014 is 14.

Also check out the Least Common Multiple of 35000 and 35014