Question

Write the sum of the number$40 + 25$ as the product of their GCF and another sum.

Answer 1

Hint: The full form of GCF is the greatest common factor. GCF is found by using the prime factorization method. Firstly, we need to find the prime factors of each number and then circle the numbers that are common in each number and the multiplication of all the circled numbers is the greatest common factor.

Complete step by step solution:
The numbers given here are $40$ and $25$, firstly we need to find the prime factors of the numbers. Prime factors of$40$ are,
$40 = 2 \times 2 \times 2 \times 5$
Prime factors of $25$ are,
$25 = 5 \times 5$
Now, we have to identify the common factors by circle out the common factor in each term and now we have found that there is a single common factor i.e,$5$. Here, $5$ is the GCF of the given numbers. Now, we have $40 + 25$ and now, we will take $5$ common, from both the numbers as $5$ is common in both. Then, the number can be written as,
$5\left( {8 + 5} \right)$ .

Thus, we have shown that the sum of the number $40 + 25$ is the product of their GCF and another sum.$

Note: When another number is produced by multiplying the whole numbers with each other, then these whole numbers are termed to as factors. Let us take an example, $a \times b = c$, here a and b are the factors of c and when the number is broken down into the set of prime numbers and the multiplication of these prime numbers form the original number is known as prime factorization.