What is the Greatest Common Factor of 35700 and 35705?

Greatest common factor (GCF) of 35700 and 35705 is 5.

GCF(35700,35705) = 5

We will now calculate the prime factors of 35700 and 35705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35700 and 35705.

How to find the GCF of 35700 and 35705?

We will first find the prime factorization of 35700 and 35705. After we will calculate the factors of 35700 and 35705 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 35705

Prime factors of 35705 are 5, 37, 193. Prime factorization of 35705 in exponential form is:

35705 = 5¹ × 37¹ × 193¹

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 35705

List of positive integer factors of 35705 that divides 35700 without a remainder.

1, 5, 37, 185, 193, 965, 7141

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35700 and 35705. The biggest common factor number is the GCF number.
So the greatest common factor 35700 and 35705 is 5.

Also check out the Least Common Multiple of 35700 and 35705