What is the Greatest Common Factor of 69720 and 69729?

Greatest common factor (GCF) of 69720 and 69729 is 3.

GCF(69720,69729) = 3

We will now calculate the prime factors of 69720 and 69729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69720 and 69729.

How to find the GCF of 69720 and 69729?

We will first find the prime factorization of 69720 and 69729. After we will calculate the factors of 69720 and 69729 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 69729

Prime factors of 69729 are 3, 11, 2113. Prime factorization of 69729 in exponential form is:

69729 = 3¹ × 11¹ × 2113¹

Step-3: Factors of 69720

List of positive integer factors of 69720 that divides 69720 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

Step-4: Factors of 69729

List of positive integer factors of 69729 that divides 69720 without a remainder.

1, 3, 11, 33, 2113, 6339, 23243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69720 and 69729. The biggest common factor number is the GCF number.
So the greatest common factor 69720 and 69729 is 3.

Also check out the Least Common Multiple of 69720 and 69729