What is the Greatest Common Factor of 69705 and 69720?

Greatest common factor (GCF) of 69705 and 69720 is 15.

GCF(69705,69720) = 15

We will now calculate the prime factors of 69705 and 69720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69705 and 69720.

How to find the GCF of 69705 and 69720?

We will first find the prime factorization of 69705 and 69720. After we will calculate the factors of 69705 and 69720 and find the biggest common factor number .

Step-1: Prime Factorization of 69705

Prime factors of 69705 are 3, 5, 1549. Prime factorization of 69705 in exponential form is:

69705 = 3² × 5¹ × 1549¹

Step-2: Prime Factorization of 69720

Prime factors of 69720 are 2, 3, 5, 7, 83. Prime factorization of 69720 in exponential form is:

69720 = 2³ × 3¹ × 5¹ × 7¹ × 83¹

Step-3: Factors of 69705

List of positive integer factors of 69705 that divides 69705 without a remainder.

1, 3, 5, 9, 15, 45, 1549, 4647, 7745, 13941, 23235

Step-4: Factors of 69720

List of positive integer factors of 69720 that divides 69705 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 83, 84, 105, 120, 140, 166, 168, 210, 249, 280, 332, 415, 420, 498, 581, 664, 830, 840, 996, 1162, 1245, 1660, 1743, 1992, 2324, 2490, 2905, 3320, 3486, 4648, 4980, 5810, 6972, 8715, 9960, 11620, 13944, 17430, 23240, 34860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69705 and 69720. The biggest common factor number is the GCF number.
So the greatest common factor 69705 and 69720 is 15.

Also check out the Least Common Multiple of 69705 and 69720