Question

Check whether 357 is divisible by 17 or not.

Answer 1

Hint: For solving this question we will first find the factors of 357. And if 17 will be one of the factors of 357 then we will say that 357 is divisible by 17 otherwise not.
Complete step by step answer:
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 till 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, we will express 357 in terms of multiplication of prime numbers. Then we will find the factors of 357 which will give us a total list of numbers by which 357 can be divided.
We can write, $357=1\times 3\times 7\times 17$ . Then,
Factors of 357 are: 1, 3, 7, 17, 21, 51, 119 and 357.
Now, in the list of factors of 357 as 17 is there so, we conclude that 357 is divisible by 17.
Hence, 357 is divisible by 17.

Note: The problem was very easy to solve but we could have solved this by another method also and that is by checking by divisibility rule for 17 which states that for a number to be divisible by 17 we have to subtract the 5 times of the unit digit from the truncated number then the result should be divisible by 17. We have to apply this rule over and over again till we conclude. For example: in this question $35-7\times 5=0$ . That’s why 357 is divisible by 17.