Name: Prime Numbers & Prime Factorisation
Uploaded: 2019-07-19
Duration: 6 min 40 s
Description: In this video, we will learn the concept of factors, prime numbers, and prime factorisation methods of finding numbers with examples.

Question

If the

8

-digit number

136 x 5785

is divisible by

15

, then find the least possible value of

x

.

Accepted Answer

Given
The $8$ -digit number is $136 x 5785$ is divisible by $15$ .
To find the least possible value of $x$

Let us get the prime factorization of $15$
$15 = 3 \times 5$
If the number to be divisible by $15$ , it must be divisible by both $3$ and $5 .$
To be divisible by $3$ , sum of the numbers must be divisible by $3$ .
To be divisible by $5$ , units digit must be $0$ or $5$ .

$136 x 5785$ is divisible by $5$ regardless of the values of $x$
For $136 x 5785$ to be divisible by $3, 1 + 3 + 6 + x + 5 + 7 + 8 + 5$ must be divisible by $3$
$= 35 + x$ must be divisible by $3$

If we add $1$ to the $35$ the number is divisible by $3$ .
$\Rightarrow 35 + 1 = 36$ is divisible by $3$ .

Therefore, the least value of $x = 1$

Manisha Paul Solutions for Chapter: Factors and Multiples, Exercise 9: High Order Thinking Skills (HOTS)

Manisha Paul Mathematics Solutions for Exercise - Manisha Paul Solutions for Chapter: Factors and Multiples, Exercise 9: High Order Thinking Skills (HOTS)

Questions from Manisha Paul Solutions for Chapter: Factors and Multiples, Exercise 9: High Order Thinking Skills (HOTS) with Hints & Solutions

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