What is the Greatest Common Factor of 69720 and 69734?

Greatest common factor (GCF) of 69720 and 69734 is 14.

GCF(69720,69734) = 14

We will now calculate the prime factors of 69720 and 69734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69720 and 69734.

How to find the GCF of 69720 and 69734?

We will first find the prime factorization of 69720 and 69734. After we will calculate the factors of 69720 and 69734 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 69734

Prime factors of 69734 are 2, 7, 17, 293. Prime factorization of 69734 in exponential form is:

69734 = 2¹ × 7¹ × 17¹ × 293¹

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 69734

List of positive integer factors of 69734 that divides 69720 without a remainder.

1, 2, 7, 14, 17, 34, 119, 238, 293, 586, 2051, 4102, 4981, 9962, 34867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69720 and 69734. The biggest common factor number is the GCF number.
So the greatest common factor 69720 and 69734 is 14.

Also check out the Least Common Multiple of 69720 and 69734