Question

Write 98 as a product of its prime factors.

Answer 1

Hint: Here, we will be using the concept of prime factorisation of numbers. Prime factorisation is the method of finding the prime factors of the given number.

Complete step-by-step answer:
We know that in the number system, prime numbers are the numbers which have only two factors, 1 and the number itself. Hence, it is obvious that they will be divisible by 1 and the number itself.
Now, the given number is 98. Let us find its divisibility by the prime divisors, starting with the smallest prime number, which is 2.
We observe that the number 98 is an even number. Hence, it is divisible by 2.
$${\displaystyle \frac{98}{2}}=49$$
Next, we sum up the digits of the result 49.
Hence, we get $$4+9=13$$.
We see that the sum of the digits of the given number is not divisible by 3.
So, the number is not divisible by 3.
Now, the last digit of the number 49 is neither 0 nor 5.
Thus, the number 49 is not divisible by 5.
Now, we check the divisibility of the number by 7. To check divisibility by 7, twice the unit’s place digit subtracted from the rest of the number should be divisible by 7.
Here, twice the unit’s place digit is $$9\times 2=18$$.
We subtract 18 from the remaining number 4 to check whether 49 is divisible by 7.
$$4-18=-14$$
Now, the number $$-14$$ is divisible by 7.
Hence, the number 49 is divisible by 7.
Thus, dividing 49 by 7, we get
$$\frac{49}{7}=7$$
Hence, resolving into factors, we get that 98 can be expressed as
$$98=2\times 7\times 7$$

In this expression, 98 is expressed as a product of its prime factors 2, 7 and 7.

Note: In these types of problems, it should always be remembered that it is important to know the rules of divisibility to find the prime factors of a given number. For checking divisibility by smaller prime numbers, in most cases, it is not required to actually divide the number by the prime number, but we can apply the rules of divisibility effectively.