What is the Greatest Common Factor of 69984 and 70004?

Greatest common factor (GCF) of 69984 and 70004 is 4.

GCF(69984,70004) = 4

We will now calculate the prime factors of 69984 and 70004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69984 and 70004.

How to find the GCF of 69984 and 70004?

We will first find the prime factorization of 69984 and 70004. After we will calculate the factors of 69984 and 70004 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 70004

Prime factors of 70004 are 2, 11, 37, 43. Prime factorization of 70004 in exponential form is:

70004 = 2² × 11¹ × 37¹ × 43¹

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 70004

List of positive integer factors of 70004 that divides 69984 without a remainder.

1, 2, 4, 11, 22, 37, 43, 44, 74, 86, 148, 172, 407, 473, 814, 946, 1591, 1628, 1892, 3182, 6364, 17501, 35002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69984 and 70004. The biggest common factor number is the GCF number.
So the greatest common factor 69984 and 70004 is 4.

Also check out the Least Common Multiple of 69984 and 70004