Question

The greatest factor of 12 is the smallest multiple of

Answer 1

Hint: We can list out all the factors of 12 and find the greatest one from it. Then we can write the greatest factor as the multiples of its factors. The smallest multiple out of them which give the greatest factor will be the required answer.

Complete step by step answer:

We have the number 12. We can find the factors of 12 by checking which all numbers give remainder zero when dividing 12 with it.
We can check whether 1 is a factor of 12. We know that 12 is divisible by 1. So, 1 is a factor of 12.
Then we have$12 \times 1 = 12$. So 12 is also a factor of 12
Now we can check whether 2 is a factor of 12. We know that 12 is divisible by 2 and give 6 as quotient. So we have$6 \times 2 = 12$. Therefore 6 is also a factor of 12.
Now we can check whether 3 is a factor of 12. We know that 12 is divisible by 3 and give 4 as quotient. So we have$4 \times 3 = 12$. Therefore 4 is also a factor of 12.
The next number is 4. But we already found that it is a factor. So we can stop here.
Therefore, the factors of \[12\] are 1, 2, 3,4, 6, and 12. Out of these factors, the greatest factor is 12.
Now we need to find the number whose smallest multiple is 12.
So, we can write multiple of the factors of 12.
For 1, the multiples are, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 11, 12
For 2, the multiples are, 2, 4, 6, 8, 10, 12
For 3, the multiples are, 3, 6, 9, 12
For 4, the multiples are, 4, 8, 12
For 6, the multiples are, 6, 12
For 12, the multiples are, 12
From the above multiples, we can understand that 12 is the smallest multiple of 12 itself.
Therefore, the greatest factor of 12 is the smallest multiple of 12.

Note: Factors of a number are the numbers which on multiplication gives that particular number. The greatest factor of a number is the factor with the highest value. For any number, its greatest factor is the number itself. Multiples of a number are the numbers that can be divided by that number a certain number of times without leaving a remainder. For any two numbers a and b, a is a multiple of b if $a = nb$ where n is an integer. We can also say that n and b are factors of a. The smallest multiple of a number is the number itself. The smallest common multiple of two numbers is the smallest number which is completely divisible by both the numbers.