What is the Greatest Common Factor of 48195 and 48209?

Greatest common factor (GCF) of 48195 and 48209 is 7.

GCF(48195,48209) = 7

We will now calculate the prime factors of 48195 and 48209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48195 and 48209.

How to find the GCF of 48195 and 48209?

We will first find the prime factorization of 48195 and 48209. After we will calculate the factors of 48195 and 48209 and find the biggest common factor number .

Step-1: Prime Factorization of 48195

Prime factors of 48195 are 3, 5, 7, 17. Prime factorization of 48195 in exponential form is:

48195 = 3⁴ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 48209

Prime factors of 48209 are 7, 71, 97. Prime factorization of 48209 in exponential form is:

48209 = 7¹ × 71¹ × 97¹

Step-3: Factors of 48195

List of positive integer factors of 48195 that divides 48195 without a remainder.

1, 3, 5, 7, 9, 15, 17, 21, 27, 35, 45, 51, 63, 81, 85, 105, 119, 135, 153, 189, 255, 315, 357, 405, 459, 567, 595, 765, 945, 1071, 1377, 1785, 2295, 2835, 3213, 5355, 6885, 9639, 16065

Step-4: Factors of 48209

List of positive integer factors of 48209 that divides 48195 without a remainder.

1, 7, 71, 97, 497, 679, 6887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48195 and 48209. The biggest common factor number is the GCF number.
So the greatest common factor 48195 and 48209 is 7.

Also check out the Least Common Multiple of 48195 and 48209