Question

Compute the prime factorization of: gcd(25735718750,
6860000)

Answer 1

To compute the prime factorization of the gcd of two numbers, find the prime factorization of each number and identify the common factors. Take the lowest power of each common factor to obtain the gcd.

Step-by-step explanation:

To compute the prime factorization of the greatest common divisor (gcd) of 25735718750 and 6860000, we can use the prime factorization method. First, let's find the prime factorization of both numbers:

25735718750: 2 × 55 × 7 × 73 × 6311

6860000: 24 × 53 × 7 × 11 × 13

Next, we identify common prime factors between the two numbers and take the lowest power of each common factor. The common prime factors between 25735718750 and 6860000 are 2, 5, and 7. Taking the lowest power of each, we have:

gcd(25735718750, 6860000) = 2 × 53 × 7 = 3500.