What is the Greatest Common Factor of 29664 and 29670?

Greatest common factor (GCF) of 29664 and 29670 is 6.

GCF(29664,29670) = 6

We will now calculate the prime factors of 29664 and 29670, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29664 and 29670.

How to find the GCF of 29664 and 29670?

We will first find the prime factorization of 29664 and 29670. After we will calculate the factors of 29664 and 29670 and find the biggest common factor number .

Step-1: Prime Factorization of 29664

Prime factors of 29664 are 2, 3, 103. Prime factorization of 29664 in exponential form is:

29664 = 2⁵ × 3² × 103¹

Step-2: Prime Factorization of 29670

Prime factors of 29670 are 2, 3, 5, 23, 43. Prime factorization of 29670 in exponential form is:

29670 = 2¹ × 3¹ × 5¹ × 23¹ × 43¹

Step-3: Factors of 29664

List of positive integer factors of 29664 that divides 29664 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 103, 144, 206, 288, 309, 412, 618, 824, 927, 1236, 1648, 1854, 2472, 3296, 3708, 4944, 7416, 9888, 14832

Step-4: Factors of 29670

List of positive integer factors of 29670 that divides 29664 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 43, 46, 69, 86, 115, 129, 138, 215, 230, 258, 345, 430, 645, 690, 989, 1290, 1978, 2967, 4945, 5934, 9890, 14835

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29664 and 29670. The biggest common factor number is the GCF number.
So the greatest common factor 29664 and 29670 is 6.

Also check out the Least Common Multiple of 29664 and 29670