What is the Greatest Common Factor of 69209 and 69216?

Greatest common factor (GCF) of 69209 and 69216 is 7.

GCF(69209,69216) = 7

We will now calculate the prime factors of 69209 and 69216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69209 and 69216.

How to find the GCF of 69209 and 69216?

We will first find the prime factorization of 69209 and 69216. After we will calculate the factors of 69209 and 69216 and find the biggest common factor number .

Step-1: Prime Factorization of 69209

Prime factors of 69209 are 7, 9887. Prime factorization of 69209 in exponential form is:

69209 = 7¹ × 9887¹

Step-2: 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-3: Factors of 69209

List of positive integer factors of 69209 that divides 69209 without a remainder.

1, 7, 9887

Step-4: Factors of 69216

List of positive integer factors of 69216 that divides 69209 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69209 and 69216. The biggest common factor number is the GCF number.
So the greatest common factor 69209 and 69216 is 7.

Also check out the Least Common Multiple of 69209 and 69216