What is the Greatest Common Factor of 69216 and 69225?

Greatest common factor (GCF) of 69216 and 69225 is 3.

GCF(69216,69225) = 3

We will now calculate the prime factors of 69216 and 69225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69216 and 69225.

How to find the GCF of 69216 and 69225?

We will first find the prime factorization of 69216 and 69225. After we will calculate the factors of 69216 and 69225 and find the biggest common factor number .

Step-1: Prime Factorization of 69216

Prime factors of 69216 are 2, 3, 7, 103. Prime factorization of 69216 in exponential form is:

69216 = 2⁵ × 3¹ × 7¹ × 103¹

Step-2: Prime Factorization of 69225

Prime factors of 69225 are 3, 5, 13, 71. Prime factorization of 69225 in exponential form is:

69225 = 3¹ × 5² × 13¹ × 71¹

Step-3: Factors of 69216

List of positive integer factors of 69216 that divides 69216 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 103, 112, 168, 206, 224, 309, 336, 412, 618, 672, 721, 824, 1236, 1442, 1648, 2163, 2472, 2884, 3296, 4326, 4944, 5768, 8652, 9888, 11536, 17304, 23072, 34608

Step-4: Factors of 69225

List of positive integer factors of 69225 that divides 69216 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 71, 75, 195, 213, 325, 355, 923, 975, 1065, 1775, 2769, 4615, 5325, 13845, 23075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69216 and 69225. The biggest common factor number is the GCF number.
So the greatest common factor 69216 and 69225 is 3.

Also check out the Least Common Multiple of 69216 and 69225