What is the Greatest Common Factor of 31946 and 31960?

Greatest common factor (GCF) of 31946 and 31960 is 2.

GCF(31946,31960) = 2

We will now calculate the prime factors of 31946 and 31960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31946 and 31960.

How to find the GCF of 31946 and 31960?

We will first find the prime factorization of 31946 and 31960. After we will calculate the factors of 31946 and 31960 and find the biggest common factor number .

Step-1: Prime Factorization of 31946

Prime factors of 31946 are 2, 15973. Prime factorization of 31946 in exponential form is:

31946 = 2¹ × 15973¹

Step-2: Prime Factorization of 31960

Prime factors of 31960 are 2, 5, 17, 47. Prime factorization of 31960 in exponential form is:

31960 = 2³ × 5¹ × 17¹ × 47¹

Step-3: Factors of 31946

List of positive integer factors of 31946 that divides 31946 without a remainder.

1, 2, 15973

Step-4: Factors of 31960

List of positive integer factors of 31960 that divides 31946 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 47, 68, 85, 94, 136, 170, 188, 235, 340, 376, 470, 680, 799, 940, 1598, 1880, 3196, 3995, 6392, 7990, 15980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31946 and 31960. The biggest common factor number is the GCF number.
So the greatest common factor 31946 and 31960 is 2.

Also check out the Least Common Multiple of 31946 and 31960