Question

13 and 64 pairs of numbers are co-primes?​

Answer 1

SoluTioN -

Step 1 -

• Divide the larger number by the smaller one:
• 64 ÷ 13 = 4 + 12;

Step 2 -

• Divide the smaller number by the above operation's remainder:
• 13 ÷ 12 = 1 + 1;

Step 3 -

• Divide the remainder from the step 1 by the remainder from the step 2:
• 12 ÷ 1 = 12 + 0
• At this step, the remainder is zero, so we stop:
• 1 is the number we were looking for, the last remainder that is not zero.

$\rightarrow$ This is the greatest common factor (divisor).

• gcf, hcf, gcd (13; 64) = 1;

$\rightarrow$Coprime numbers (relatively prime) (13; 64)

gcf, hcf, gcd (13; 64) = 1. ㅤㅤ── Euclid's algorithm

$\rightarrow$Final answer

13 and 64 are coprime (relatively, mutually prime) - if they have no common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is 1.

$\large\therefore \: 13 \: and \: 64 \: are \: co \: primes$