What is the Greatest Common Factor of 35686 and 35700?

Greatest common factor (GCF) of 35686 and 35700 is 14.

GCF(35686,35700) = 14

We will now calculate the prime factors of 35686 and 35700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35686 and 35700.

How to find the GCF of 35686 and 35700?

We will first find the prime factorization of 35686 and 35700. After we will calculate the factors of 35686 and 35700 and find the biggest common factor number .

Step-1: Prime Factorization of 35686

Prime factors of 35686 are 2, 7, 2549. Prime factorization of 35686 in exponential form is:

35686 = 2¹ × 7¹ × 2549¹

Step-2: 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-3: Factors of 35686

List of positive integer factors of 35686 that divides 35686 without a remainder.

1, 2, 7, 14, 2549, 5098, 17843

Step-4: Factors of 35700

List of positive integer factors of 35700 that divides 35686 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35686 and 35700. The biggest common factor number is the GCF number.
So the greatest common factor 35686 and 35700 is 14.

Also check out the Least Common Multiple of 35686 and 35700