using verticle method to find the HCF of 230,322
Answers
230 = 2 × 5 × 23;
322 = 2 × 7 × 23;
Multiply all the common prime factors, by the lowest exponents.
Greatest (highest) common factor (divisor):
gcf, hcf, gcd (230; 322) = 2 × 23
gcf, hcf, gcd (230; 322) = 2 × 23 = 46;
the numbers have common prime factors
Integer numbers prime factorization
Approach 2. Euclid's algorithm:
Step 1. Divide the larger number by the smaller one:
322 ÷ 230 = 1 + 92;
Step 2. Divide the smaller number by the above operation's remainder:
230 ÷ 92 = 2 + 46;
Step 3. Divide the remainder from the step 1 by the remainder from the step 2:
92 ÷ 46 = 2 + 0;
At this step, the remainder is zero, so we stop:
46 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, hcf, gcd (230; 322) = 46
gcf, hcf, gcd (230; 322) = 46 = 2 × 23;