What is the greatest common factor of 63 and 105?
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What is the GCF of 63 and 105?
The first step to find the gcf of 63 and 105 is to list the factors of each number. The factors of 63 are 1, 3, 7, 9, 21 and 63. The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105. So, the Greatest Common Factor for these numbers is 21 because it divides all them without a remainder. Read more about Common Factors below.
To use the GCD / GCF / HCF Calculator below just enter a set of numbers separated by commas (,).
How to find the Greatest Common Factor
The first step is to find all divisors of each number. For instance, let us find the gcf(63,105).
In this case we have:
- The factors of 63 (all the whole numbers that can divide the number without a remainder) are 1, 3, 7, 9, 21 and 63;
- The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.
The second step is to analyze which are the common divisors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 63 and 105 is 21. The GCF is the largest common positive integer that divides all the numbers (63,105) without a remainder.
The GCF is also known as:
- Greatest common divisor (gcd);
- Highest common factor (hcf);
- Greatest common measure (gcm), or
- Highest common divisor