What is the Greatest Common Factor of 35084 and 35100?

Greatest common factor (GCF) of 35084 and 35100 is 4.

GCF(35084,35100) = 4

We will now calculate the prime factors of 35084 and 35100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35084 and 35100.

How to find the GCF of 35084 and 35100?

We will first find the prime factorization of 35084 and 35100. After we will calculate the factors of 35084 and 35100 and find the biggest common factor number .

Step-1: Prime Factorization of 35084

Prime factors of 35084 are 2, 7, 179. Prime factorization of 35084 in exponential form is:

35084 = 2² × 7² × 179¹

Step-2: Prime Factorization of 35100

Prime factors of 35100 are 2, 3, 5, 13. Prime factorization of 35100 in exponential form is:

35100 = 2² × 3³ × 5² × 13¹

Step-3: Factors of 35084

List of positive integer factors of 35084 that divides 35084 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 179, 196, 358, 716, 1253, 2506, 5012, 8771, 17542

Step-4: Factors of 35100

List of positive integer factors of 35100 that divides 35084 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 27, 30, 36, 39, 45, 50, 52, 54, 60, 65, 75, 78, 90, 100, 108, 117, 130, 135, 150, 156, 180, 195, 225, 234, 260, 270, 300, 325, 351, 390, 450, 468, 540, 585, 650, 675, 702, 780, 900, 975, 1170, 1300, 1350, 1404, 1755, 1950, 2340, 2700, 2925, 3510, 3900, 5850, 7020, 8775, 11700, 17550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35084 and 35100. The biggest common factor number is the GCF number.
So the greatest common factor 35084 and 35100 is 4.

Also check out the Least Common Multiple of 35084 and 35100