Question

State the following statement is true or false
The HCF of 90 and 162 is 18.

Answer 1

Hint: HCF of two numbers is the highest common factor dividing both the numbers.
Therefore, first we will calculate the factors of both the given numbers using the prime factorization method and then find the highest factor which divides both the numbers.
Prime factorization method is the method of factoring a number into the product of prime numbers.

Complete step-by-step answer:
Here first we will calculate the factors of 90 and 162
Therefore, calculating the factors of 90 using prime factorization method we get:-
\[90 = 2 \times 3 \times 3 \times 5\]
Now calculating the factors of 162 using prime factorization method we get:-
\[162 = 2 \times 3 \times 3 \times 3 \times 3\]
Now we will find the highest common factor dividing both the numbers by making the pairs of factors common to both the numbers and multiplying only those numbers in pairs by writing them once to get the answer.

\[90 = \] \[2 \times \] \[3 \times \] \[3 \times \] \[5\]
\[162 = \] \[2 \times \] \[3 \times \] \[3 \times \] \[3 \times \] \[3\]

Hence we get the HCF of 90 and 162 as:-
\[
  HCF = 2 \times 3 \times 3 \\
  HCF = 6 \times 3 \\
  HCF = 18 \\
 \]
Also the given HCF is 18
Hence the statement The HCF of 90 and 162 is 18 is TRUE.

Note: Students can also calculate the factors of both the numbers using factor tree and then calculate the HCF.
The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring. These two factors are the first branching in the factor tree.
We repeat the process with each factor until each branch of the tree ends in a prime number.
The factors of 90 using factor tree can be calculated as:-

               

Hence the factors of 90 are: 2,5,3,3
Similarly, the factors of 162 using factor tree can be calculated as:-

                    

Hence the factors of 162 are: 2,3,3,3,3