Step 1. Divide the larger number by the smaller one:
19,909 ÷ 10,063 = 1 + 9,846
Step 2. Divide the smaller number by the above operation's remainder:
10,063 ÷ 9,846 = 1 + 217
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
9,846 ÷ 217 = 45 + 81
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
217 ÷ 81 = 2 + 55
Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
81 ÷ 55 = 1 + 26
Step 6. Divide the remainder of the step 4 by the remainder of the step 5:
55 ÷ 26 = 2 + 3
Step 7. Divide the remainder of the step 5 by the remainder of the step 6:
26 ÷ 3 = 8 + 2
Step 8. Divide the remainder of the step 6 by the remainder of the step 7:
3 ÷ 2 = 1 + 1
Step 9. Divide the remainder of the step 7 by the remainder of the step 8:
2 ÷ 1 = 2 + 0
At this step, the remainder is zero, so we stop:
1 is the number we were looking for - the last non-zero remainder.
This is the greatest (highest) common factor (divisor).
The greatest (highest) common factor (divisor):
gcf, hcf, gcd (19,909; 10,063) = 1
Coprime numbers (prime to each other, relatively prime).
The two numbers have no prime factors in common
Why do we need to calculate the greatest common factor?
Once you've calculated the greatest common factor of the numerator and the denominator of a fraction, it becomes much easier to fully reduce (simplify) the fraction to the lowest terms (the smallest possible numerator and denominator).