Question

How do you write the sum of the numbers \[24 + 40\] as the product of their GCF and another sum?

Answer 1

Hint: GCF means greatest common factor. The greatest number that is a factor of two (or more) other numbers. First we find the prime factors of 24 and 40. Using prime factors we can find the greatest common factor and taking in the greatest common factor number we will have the desired result. Prime number is a number which is divisible by 1 and itself.

Complete step by step solution:
Given, \[24 + 40\].
Now the prime factors of 24 are 2 multiplied 3 times and 3.
That is
\[24 = 2 \times 2 \times 2 \times 3\]
Now the prime factors of 40 are 2 multiplied 3 times and 5.
That is
\[40 = 2 \times 2 \times 2 \times 5\]
Thus we can see that the greatest common factor is \[2 \times 2 \times 2 = 8\].
Hence GCF is 8.
Now we have, \[24 + 40\]
Take 8 common we have
\[24 + 40 = 8(3 + 5)\]
Thus we have expressed \[24 + 40\] as the product of their GCF and another sum.

Note: In the above we used a repeated division method. As the name suggests in this method we begin by dividing the number with its smallest prime factor until we reach 1 as the final quotient.
This is what we did in the above problem. 24 is divided by 2 we have remainder 12. We divide 12 by 2 we have remainder 6. We divide 6 by 2 we get the remainder 3. We divide 3 by 3 we get remainder
We stop here. We did the same thing for 40 also. Here we note that ‘2’ is a prime number.