What is the Greatest Common Factor of 69969 and 69984?

Greatest common factor (GCF) of 69969 and 69984 is 3.

GCF(69969,69984) = 3

We will now calculate the prime factors of 69969 and 69984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69969 and 69984.

How to find the GCF of 69969 and 69984?

We will first find the prime factorization of 69969 and 69984. After we will calculate the factors of 69969 and 69984 and find the biggest common factor number .

Step-1: Prime Factorization of 69969

Prime factors of 69969 are 3, 83, 281. Prime factorization of 69969 in exponential form is:

69969 = 3¹ × 83¹ × 281¹

Step-2: Prime Factorization of 69984

Prime factors of 69984 are 2, 3. Prime factorization of 69984 in exponential form is:

69984 = 2⁵ × 3⁷

Step-3: Factors of 69969

List of positive integer factors of 69969 that divides 69969 without a remainder.

1, 3, 83, 249, 281, 843, 23323

Step-4: Factors of 69984

List of positive integer factors of 69984 that divides 69969 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 729, 864, 972, 1296, 1458, 1944, 2187, 2592, 2916, 3888, 4374, 5832, 7776, 8748, 11664, 17496, 23328, 34992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69969 and 69984. The biggest common factor number is the GCF number.
So the greatest common factor 69969 and 69984 is 3.

Also check out the Least Common Multiple of 69969 and 69984