Question

what is the greatest number hcf of 1800 and 4200

Answer 1

Approach 1. Integer numbers prime factorization:
4,200 = 23 × 3 × 52 × 7;
1,800 = 23 × 32 × 52;
Take all the common prime factors, by the lowest exponents.
Greatest (highest) common factor (divisor)
gcf, gcd (4,200; 1,800) = 23 × 3 × 52 = 600;
Approach 2. Euclid's algorithm:
Step 1. Divide the larger number by the smaller one:
4,200 ÷ 1,800 = 2 + 600;
Step 2. Divide the smaller number by the above operation's remainder:
1,800 ÷ 600 = 3 + 0;
At this step, the remainder is zero, so we stop:
600 is the number we were looking for, the last remainder that is not zero.
This is the greatest common factor (divisor).
Greatest (highest) common factor (divisor)
gcf, gcd (4,200; 1,800) = 600 = 23 × 3 × 52;
Final answer:


Greatest (highest) common factor (divisor)
gcf, gcd (4,200; 1,800) = 600 = 23 × 3 × 52;
Numbers have common prime factors.