What is the Greatest Common Factor of 29670 and 29680?

Greatest common factor (GCF) of 29670 and 29680 is 10.

GCF(29670,29680) = 10

We will now calculate the prime factors of 29670 and 29680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29670 and 29680.

How to find the GCF of 29670 and 29680?

We will first find the prime factorization of 29670 and 29680. After we will calculate the factors of 29670 and 29680 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 29680

Prime factors of 29680 are 2, 5, 7, 53. Prime factorization of 29680 in exponential form is:

29680 = 2⁴ × 5¹ × 7¹ × 53¹

Step-3: Factors of 29670

List of positive integer factors of 29670 that divides 29670 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

Step-4: Factors of 29680

List of positive integer factors of 29680 that divides 29670 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 53, 56, 70, 80, 106, 112, 140, 212, 265, 280, 371, 424, 530, 560, 742, 848, 1060, 1484, 1855, 2120, 2968, 3710, 4240, 5936, 7420, 14840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29670 and 29680. The biggest common factor number is the GCF number.
So the greatest common factor 29670 and 29680 is 10.

Also check out the Least Common Multiple of 29670 and 29680