What is the Greatest Common Factor of 32940 and 32960?

Greatest common factor (GCF) of 32940 and 32960 is 20.

GCF(32940,32960) = 20

We will now calculate the prime factors of 32940 and 32960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32940 and 32960.

How to find the GCF of 32940 and 32960?

We will first find the prime factorization of 32940 and 32960. After we will calculate the factors of 32940 and 32960 and find the biggest common factor number .

Step-1: Prime Factorization of 32940

Prime factors of 32940 are 2, 3, 5, 61. Prime factorization of 32940 in exponential form is:

32940 = 2² × 3³ × 5¹ × 61¹

Step-2: Prime Factorization of 32960

Prime factors of 32960 are 2, 5, 103. Prime factorization of 32960 in exponential form is:

32960 = 2⁶ × 5¹ × 103¹

Step-3: Factors of 32940

List of positive integer factors of 32940 that divides 32940 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 61, 90, 108, 122, 135, 180, 183, 244, 270, 305, 366, 540, 549, 610, 732, 915, 1098, 1220, 1647, 1830, 2196, 2745, 3294, 3660, 5490, 6588, 8235, 10980, 16470

Step-4: Factors of 32960

List of positive integer factors of 32960 that divides 32940 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 103, 160, 206, 320, 412, 515, 824, 1030, 1648, 2060, 3296, 4120, 6592, 8240, 16480

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32940 and 32960. The biggest common factor number is the GCF number.
So the greatest common factor 32940 and 32960 is 20.

Also check out the Least Common Multiple of 32940 and 32960