Question

Write the factors of 35 in multiplication form.

Answer 1

Hint: Try to recall the definition of factors which states that factors are those numbers which completely divides the given number and leaves and leaves the remainder zero.

Complete step-by-step solution -
Before proceeding with the solution, let’s understand the concept of prime factorization. A prime number is a number which is not divisible by any other number except 1 and itself. Any number can be expressed as a product of prime numbers. All the prime numbers, which when multiplied, give a product equal to a number (say x) are called the prime factors of the number x. To write the prime factors of a number, we should always start with the smallest prime number, i.e. 2 and check divisibility. If the number is divisible by the prime number, then we write the number as a product of the prime number and another number, which will be the quotient when the given number is divided by the prime number. Then, we take the quotient and repeat the same process. This process is repeated until we are left with 1 as the quotient.
For example: Consider the number 51. It is an even number. So, it is not divisible by 2. The sum of the digits of 51 is 5 + 1 = 6. Hence, 51 is divisible by 3. Now, $51=3\times 17$ . Now, we take 17. We know, 17 is a prime number. Hence, the prime factors of 51 are 3 and 17.
Now starting with finding the factors of 35. 5 is an odd number so it is not divisible by 2. Also, as the sum of the digits of the number 35 is equal to 8, and 8 is not divisible by 3, so 35 is not divisible by three as well. Now, the next prime after 3 is 5 and we can observe that 35 is definitely divisible by 5, so 35 can be written as $35=5\times 7$.
Now 5 and 7 both are primes, so 35 cannot be further simplified. Therefore, the prime factors of 35 are 5,1,35, and 7.

Note: Remember that 1 and the number itself are always the factors of a given number. Also, remember that the factors and prime factors are two different quantities, as we saw in the above question. 5 and 7 were the prime factors of 35, while 1, 5, 7, and 35 are the factors of 35.