What is the Greatest Common Factor of 21942 and 21960?

Greatest common factor (GCF) of 21942 and 21960 is 18.

GCF(21942,21960) = 18

We will now calculate the prime factors of 21942 and 21960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21942 and 21960.

How to find the GCF of 21942 and 21960?

We will first find the prime factorization of 21942 and 21960. After we will calculate the factors of 21942 and 21960 and find the biggest common factor number .

Step-1: Prime Factorization of 21942

Prime factors of 21942 are 2, 3, 23, 53. Prime factorization of 21942 in exponential form is:

21942 = 2¹ × 3² × 23¹ × 53¹

Step-2: Prime Factorization of 21960

Prime factors of 21960 are 2, 3, 5, 61. Prime factorization of 21960 in exponential form is:

21960 = 2³ × 3² × 5¹ × 61¹

Step-3: Factors of 21942

List of positive integer factors of 21942 that divides 21942 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 53, 69, 106, 138, 159, 207, 318, 414, 477, 954, 1219, 2438, 3657, 7314, 10971

Step-4: Factors of 21960

List of positive integer factors of 21960 that divides 21942 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21942 and 21960. The biggest common factor number is the GCF number.
So the greatest common factor 21942 and 21960 is 18.

Also check out the Least Common Multiple of 21942 and 21960