What is the Greatest Common Factor of 34986 and 35003?

Greatest common factor (GCF) of 34986 and 35003 is 17.

GCF(34986,35003) = 17

We will now calculate the prime factors of 34986 and 35003, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34986 and 35003.

How to find the GCF of 34986 and 35003?

We will first find the prime factorization of 34986 and 35003. After we will calculate the factors of 34986 and 35003 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 35003

Prime factors of 35003 are 17, 29, 71. Prime factorization of 35003 in exponential form is:

35003 = 17¹ × 29¹ × 71¹

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 35003

List of positive integer factors of 35003 that divides 34986 without a remainder.

1, 17, 29, 71, 493, 1207, 2059

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34986 and 35003. The biggest common factor number is the GCF number.
So the greatest common factor 34986 and 35003 is 17.

Also check out the Least Common Multiple of 34986 and 35003