What is the Greatest Common Factor of 35700 and 35710?

Greatest common factor (GCF) of 35700 and 35710 is 10.

GCF(35700,35710) = 10

We will now calculate the prime factors of 35700 and 35710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35700 and 35710.

How to find the GCF of 35700 and 35710?

We will first find the prime factorization of 35700 and 35710. After we will calculate the factors of 35700 and 35710 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 35710

Prime factors of 35710 are 2, 5, 3571. Prime factorization of 35710 in exponential form is:

35710 = 2¹ × 5¹ × 3571¹

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 35710

List of positive integer factors of 35710 that divides 35700 without a remainder.

1, 2, 5, 10, 3571, 7142, 17855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35700 and 35710. The biggest common factor number is the GCF number.
So the greatest common factor 35700 and 35710 is 10.

Also check out the Least Common Multiple of 35700 and 35710