What is the Greatest Common Factor of 64209 and 64224?

Greatest common factor (GCF) of 64209 and 64224 is 3.

GCF(64209,64224) = 3

We will now calculate the prime factors of 64209 and 64224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64209 and 64224.

How to find the GCF of 64209 and 64224?

We will first find the prime factorization of 64209 and 64224. After we will calculate the factors of 64209 and 64224 and find the biggest common factor number .

Step-1: Prime Factorization of 64209

Prime factors of 64209 are 3, 17, 1259. Prime factorization of 64209 in exponential form is:

64209 = 3¹ × 17¹ × 1259¹

Step-2: Prime Factorization of 64224

Prime factors of 64224 are 2, 3, 223. Prime factorization of 64224 in exponential form is:

64224 = 2⁵ × 3² × 223¹

Step-3: Factors of 64209

List of positive integer factors of 64209 that divides 64209 without a remainder.

1, 3, 17, 51, 1259, 3777, 21403

Step-4: Factors of 64224

List of positive integer factors of 64224 that divides 64209 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 223, 288, 446, 669, 892, 1338, 1784, 2007, 2676, 3568, 4014, 5352, 7136, 8028, 10704, 16056, 21408, 32112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64209 and 64224. The biggest common factor number is the GCF number.
So the greatest common factor 64209 and 64224 is 3.

Also check out the Least Common Multiple of 64209 and 64224