What is the Greatest Common Factor of 34986 and 35000?

Greatest common factor (GCF) of 34986 and 35000 is 14.

GCF(34986,35000) = 14

We will now calculate the prime factors of 34986 and 35000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34986 and 35000.

How to find the GCF of 34986 and 35000?

We will first find the prime factorization of 34986 and 35000. After we will calculate the factors of 34986 and 35000 and find the biggest common factor number .

Step-1: Prime Factorization of 34986

Prime factors of 34986 are 2, 3, 7, 17. Prime factorization of 34986 in exponential form is:

34986 = 2¹ × 3¹ × 7³ × 17¹

Step-2: 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-3: Factors of 34986

List of positive integer factors of 34986 that divides 34986 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 49, 51, 98, 102, 119, 147, 238, 294, 343, 357, 686, 714, 833, 1029, 1666, 2058, 2499, 4998, 5831, 11662, 17493

Step-4: Factors of 35000

List of positive integer factors of 35000 that divides 34986 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34986 and 35000. The biggest common factor number is the GCF number.
So the greatest common factor 34986 and 35000 is 14.

Also check out the Least Common Multiple of 34986 and 35000