Question

How do you find the GCF of 6, 15 and 24?

Answer 1

Hint: To solve this we need to know the difference between the Greatest common factor (GCF) and least common multiple (LCM). The greatest common factor (GCF) is the greatest factor that is common to two or more numbers. The greatest common factor of two (or more) numbers is the product of all the prime factors the numbers have in common.

Complete step-by-step answer:
We have, 6, 13 and 24. We write the factors of each number.
The factors of 6 are 1, 2 and 3.
That is \[6 = 1 \times 2 \times 3\] .
The factors of 15 are 1, 3 and 5.
That is \[15 = 1 \times 3 \times 5\] .
The factors of 24 are 1, 2, 2, 2 and 3.
That is \[24 = 1 \times 2 \times 3 \times 4\] .
We can see that the greatest common factor of these three numbers is \[1 \times 3 = 3\] .
Hence, GCF of 6, 15 and 24 is 3.
So, the correct answer is “3”.

Note: A common multiple is a number that is a multiple of two or more numbers. The least common multiple (LCM) of two or more numbers is the smallest number (excluding zero) that is a multiple of both of the numbers. If they ask us to find LCM of above problem then LCM of 6, 15 and 24 is given by: we know that
 \[6 = 1 \times 2 \times 3\]
 \[15 = 1 \times 5 \times 3\]
 \[24 = 1 \times 2 \times 4 \times 3\]
Then the LCM is given by \[1 \times 2 \times 4 \times 5 \times 3 = 120\] .
If they ask us to find HCF that is the highest common factor is 3.
Follow the same procedure for these kinds of problems.