Question

Find the common factors and the highest common factor of 92 and 100?

Answer 1

Hint: We start solving the problem by factoring the numbers 92 first as a product of prime numbers to find all the possible factors of 92. We then similarly factorize the number 100 as a product of prime numbers to find all the possible factors of 100. We then compare the obtained factors of both the numbers and find the common factors. We then find the highest of the obtained common factors to get the highest common factor.

Complete step by step answer:
According to the problem, we need to find the common factors and highest common factors of 92 and 100.
Let us first find the factors of the number 92.
So, we know that \[92=2\times 46\].
\[\Rightarrow 92=1\times 2\times 2\times 23\]. We know that 2 and 23 are prime numbers, so cannot be factored further.
Now, the factors of 92 are 1, 2, 4, 23, 46, 92 ---(1).
Now, let us find the factors of the number 100.
We know that $100=2\times 50$.
$\Rightarrow 100=2\times 2\times 25$.
$\Rightarrow 100=1\times 2\times 2\times 5\times 5$. We know that 2 and 5 are prime numbers, so cannot be factored further.
Now, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100 ---(2).
From equations (1) and (2), we can see that the common factors of the numbers 92 and 100 are 1, 2, 4.
We can see that 4 is the highest of the obtained common factors.
So, the highest common factor is 4.

∴ The common factors of 92 and 100 is 1, 2, 4. The highest common factor of 92 and 100 is 4.

Note: We should not forget that 1 is the factor for every positive number while solving this problem. We should factorize the numbers till the point that every obtained factor cannot be factored further. We can also find the highest common factor by dividing the product of numbers with its LCM (Least Common Multiple). Similarly, we can expect problems to find the numbers between 500 and 1000 that were exactly divisible by both the given numbers.