What is the Greatest Common Factor of 69984 and 70000?

Greatest common factor (GCF) of 69984 and 70000 is 16.

GCF(69984,70000) = 16

We will now calculate the prime factors of 69984 and 70000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69984 and 70000.

How to find the GCF of 69984 and 70000?

We will first find the prime factorization of 69984 and 70000. After we will calculate the factors of 69984 and 70000 and find the biggest common factor number .

Step-1: Prime Factorization of 69984

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

69984 = 2⁵ × 3⁷

Step-2: Prime Factorization of 70000

Prime factors of 70000 are 2, 5, 7. Prime factorization of 70000 in exponential form is:

70000 = 2⁴ × 5⁴ × 7¹

Step-3: Factors of 69984

List of positive integer factors of 69984 that divides 69984 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

Step-4: Factors of 70000

List of positive integer factors of 70000 that divides 69984 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 125, 140, 175, 200, 250, 280, 350, 400, 500, 560, 625, 700, 875, 1000, 1250, 1400, 1750, 2000, 2500, 2800, 3500, 4375, 5000, 7000, 8750, 10000, 14000, 17500, 35000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69984 and 70000. The biggest common factor number is the GCF number.
So the greatest common factor 69984 and 70000 is 16.

Also check out the Least Common Multiple of 69984 and 70000