What is the Greatest Common Factor of 35700 and 35714?

Greatest common factor (GCF) of 35700 and 35714 is 14.

GCF(35700,35714) = 14

We will now calculate the prime factors of 35700 and 35714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35700 and 35714.

How to find the GCF of 35700 and 35714?

We will first find the prime factorization of 35700 and 35714. After we will calculate the factors of 35700 and 35714 and find the biggest common factor number .

Step-1: Prime Factorization of 35700

Prime factors of 35700 are 2, 3, 5, 7, 17. Prime factorization of 35700 in exponential form is:

35700 = 2² × 3¹ × 5² × 7¹ × 17¹

Step-2: Prime Factorization of 35714

Prime factors of 35714 are 2, 7, 2551. Prime factorization of 35714 in exponential form is:

35714 = 2¹ × 7¹ × 2551¹

Step-3: Factors of 35700

List of positive integer factors of 35700 that divides 35700 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 25, 28, 30, 34, 35, 42, 50, 51, 60, 68, 70, 75, 84, 85, 100, 102, 105, 119, 140, 150, 170, 175, 204, 210, 238, 255, 300, 340, 350, 357, 420, 425, 476, 510, 525, 595, 700, 714, 850, 1020, 1050, 1190, 1275, 1428, 1700, 1785, 2100, 2380, 2550, 2975, 3570, 5100, 5950, 7140, 8925, 11900, 17850

Step-4: Factors of 35714

List of positive integer factors of 35714 that divides 35700 without a remainder.

1, 2, 7, 14, 2551, 5102, 17857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35700 and 35714. The biggest common factor number is the GCF number.
So the greatest common factor 35700 and 35714 is 14.

Also check out the Least Common Multiple of 35700 and 35714