Question

Here is the factor tree for 60. Find the missing numbers.

Answer 1

Hint: Now we know that the factor tree represents the factors of the given number. Now let us assume the missing numbers are x and y. Then we know that 2 and x are factors of 6 also we have 5 and y are factors of 10. Hence we can say that $2\times x=6$ and $5\times y=10$ . Hence solving these equations we can say find the value of x and y.

Complete step by step answer:
Now Let us understand the concept of Factors.
Now let us say we have 2 numbers 3 and 4.
Then we know that 3 × 4 = 12.
Hence we say that 3 and 4 are factors of 12.
Now similarly for any number we can find factors.
A factor tree is a diagram we use to determine the prime factors.
Prime factors are nothing but factors which are prime numbers.
Now to form a factor tree we first factorize the number and write it under the branches.
For example we have 12 = 3 × 4
Hence we write it as,

Now similarly we carry on the process till we get prime numbers.
Let us now consider the given factor tree
Let’s first name missing terms by variable x and y.

Now from the factor tree we can say that 2 and x are factors of 6
Hence we get $2\times x=6$ .
Dividing the whole equation by 2 we get, $x=3$ .
Similarly we have 5 and y are factors of 10.
Hence we have $5\times y=10$ .
Dividing the whole equation by 5 we get that $y=2$ .

Hence we get that the missing numbers are 3 and 2.

Note: Now note that the prime numbers just have 2 factors 1 and the number itself. Hence it cannot be factored further. Now factor trees for the same number can be different as we can say that $60=3\times 20$ as well as we can say $60=6\times 10$ but for every factor tree we will get the same prime factors in the end.