What is the Greatest Common Factor of 53970 and 53984?

Greatest common factor (GCF) of 53970 and 53984 is 14.

GCF(53970,53984) = 14

We will now calculate the prime factors of 53970 and 53984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53970 and 53984.

How to find the GCF of 53970 and 53984?

We will first find the prime factorization of 53970 and 53984. After we will calculate the factors of 53970 and 53984 and find the biggest common factor number .

Step-1: Prime Factorization of 53970

Prime factors of 53970 are 2, 3, 5, 7, 257. Prime factorization of 53970 in exponential form is:

53970 = 2¹ × 3¹ × 5¹ × 7¹ × 257¹

Step-2: Prime Factorization of 53984

Prime factors of 53984 are 2, 7, 241. Prime factorization of 53984 in exponential form is:

53984 = 2⁵ × 7¹ × 241¹

Step-3: Factors of 53970

List of positive integer factors of 53970 that divides 53970 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 257, 514, 771, 1285, 1542, 1799, 2570, 3598, 3855, 5397, 7710, 8995, 10794, 17990, 26985

Step-4: Factors of 53984

List of positive integer factors of 53984 that divides 53970 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 241, 482, 964, 1687, 1928, 3374, 3856, 6748, 7712, 13496, 26992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53970 and 53984. The biggest common factor number is the GCF number.
So the greatest common factor 53970 and 53984 is 14.

Also check out the Least Common Multiple of 53970 and 53984