What is the Greatest Common Factor of 35950 and 35970?

Greatest common factor (GCF) of 35950 and 35970 is 10.

GCF(35950,35970) = 10

We will now calculate the prime factors of 35950 and 35970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35950 and 35970.

How to find the GCF of 35950 and 35970?

We will first find the prime factorization of 35950 and 35970. After we will calculate the factors of 35950 and 35970 and find the biggest common factor number .

Step-1: Prime Factorization of 35950

Prime factors of 35950 are 2, 5, 719. Prime factorization of 35950 in exponential form is:

35950 = 2¹ × 5² × 719¹

Step-2: Prime Factorization of 35970

Prime factors of 35970 are 2, 3, 5, 11, 109. Prime factorization of 35970 in exponential form is:

35970 = 2¹ × 3¹ × 5¹ × 11¹ × 109¹

Step-3: Factors of 35950

List of positive integer factors of 35950 that divides 35950 without a remainder.

1, 2, 5, 10, 25, 50, 719, 1438, 3595, 7190, 17975

Step-4: Factors of 35970

List of positive integer factors of 35970 that divides 35950 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 109, 110, 165, 218, 327, 330, 545, 654, 1090, 1199, 1635, 2398, 3270, 3597, 5995, 7194, 11990, 17985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35950 and 35970. The biggest common factor number is the GCF number.
So the greatest common factor 35950 and 35970 is 10.

Also check out the Least Common Multiple of 35950 and 35970