Question

Can you find the H.C.F of 7 and 9 without using the prime factorization method? Justify your answer.

Answer 1

Hint: Use the long division method to find the H.C.F of 7 and 9. Consider 7 as the divisor and 9 as the dividend and divide 9 by 7. Now the remainder left will be considered as the divisor and 7 as the dividend and divide 7 with this new divisor. Again the new remainder will become divisor and the previous divisor will become dividend. This process will be followed till we get the remainder 0. The divisor due to which the remainder becomes 0 will be the H.C.F of two numbers.

Complete step by step solution:
Here we have been asked if we can find the H.C.F of 7 and 9 without using the prime factorization method. The answer is yes we can find the H.C.F using another method known as the long division method. Let us see each of its steps.
Step 1: - We take the two numbers and select the smaller one as the divisor and the larger one as the dividend and perform the division. So in the above case 7 is the divisor and 9 is the dividend. On performing the division we get,
$\Rightarrow 9=\left( 7\times 1 \right)+2$
Step 2: - Now, the remainder is considered as the new divisor and the previous divisor as the dividend and again the division is performed. Here, 3 is the remainder and hence the divisor while 7 becomes the dividend. So we get,
$\Rightarrow 7=\left( 2\times 3 \right)+1$
Step 3: - Again the remainder is 1 so it becomes the new divisor and 2 becomes the new dividend. So on dividing 2 by 1 we get,
$\Rightarrow 2=\left( 1\times 2 \right)+0$
We can see that we got the remainder 0 in the above step so we will stop here and the divisor of this step will be the H.C.F.

Hence the H.C.F of 7 and 9 is 1.

Note: If you want you can check the answer using the prime factorization method to find the H.C.F. In this process we will write 7 and 9 as the product of its prime factors and the H.C.F will be the product of all the common factors present in them. Since 7 is a prime number so it cannot be factored more as we write it as 7 only whereas 9 can be written as $9=3\times 3$. Clearly there are no common factors in both therefore the H.C.F will be 1.