Question

What are the factors of 24?

Answer 1

Hint: The factors of a number are those which divide the number without leaving a remainder. To find the factors of a number, we list all the numbers starting from 1, which divide the given number exactly with remainder as zero.

Complete step by step solution:
The number for which we need to find factors is 24. For a number to be a factor of 24, it must divide 24 in such a way that there is no remainder. First, let us prime factorize the number and then find non-prime factors. 24 can be factorized as follows,
$24=2\times 2\times 2\times 3$
Hence we have found that 2 and 3 are the prime factors of 24. Now, let us find the remaining factors by combining the prime factors in all possible ways. 24 can also be written as
$24=4\times 2\times 3$
Hence, even 4 is a factor of 24. Further, we get,
$24=2\times 2\times 6$
Hence, even 6 is a factor of 24. Further, we get,
$24=8\times 3$
Hence, even 8 is a factor of 24. Further, we get,
$24=12\times 2$
Hence, even 12 is a factor of 24. Finally, we get,
$24=24\times 1$
Even 1 and the number 24 itself is a factor of itself.
Therefore, we have obtained the factors of 24 as 1,2,3,4,6,8,12,24

Note: While solving this problem, one has to write down the prime factors first as it is the best and convenient method. Finding the non-prime factors first is also a valid approach, but this may lead to overlooking or missing factors. Hence it is best to find the prime factors first and then find the rest of the factors by combining the prime factors in all possible ways.