Name: Finding LCM and HCF of Real Numbers
Uploaded: 2019-07-19
Duration: 4 min 8 s
Description: In this video, we will learn the concept and method of finding the least common multiple, and highest common factor of real numbers in detail, with examples.

Question

By which number is $27720$ divisible?

Accepted Answer

The given number is $27720$ .

We need to check, by which number $27720$ is divisible.

Divisibility rule of $2$ : If the unit's place of any number has $0, 2, 4, 6$ and $8$ , then the number is completely divisible by $2$ .

Unit's place digit of $27720$ is $0$ , then this number is completely divisible by $2$ .

Divisibility rule of $3$ : If sum of all the digits of a number is divisible by $3$ , then the number is divisible by $3$ .

In $27720$ , the sum of all the digits would be $2 + 7 + 7 + 2 + 0 = 18$ , therefore the given number is divisible by $3$ .

Divisibility rule of $6$ : If any number is divisible by $2$ and $3$ separately, then the number will be divisible by $6$ .

Since, the given number is divisible by both $2$ and $3$ , it is also divisible by $6$ .

Divisibility rule of $9$ : If sum of all the digits of a number is divisible by $9$ , then the number is divisible by $9$ .

In $27720$ , the sum of all the digits would be $2 + 7 + 7 + 2 + 0 = 18$ , therefore the given number is divisible by $9$ .

Divisibility rule of $5$ : If the digit the unit's place is $0$ or $27720$ , then number will be divisible by $5$ .

Unit's place digit of $27720$ is $0$ , then this number is completely divisible by $5$ .

Divisibility rule of $10$ : If any number has $0$ in its unit's place, then the number is divisible by $10$ .

Unit's place digit of $27720$ is $0$ , then this number is completely divisible by $10$ .

Divisibility rule of $4$ : If the number made by the ten's and unit's place digits of any number is divisible by $4$ or the ten's and unit's place has zero, then the number is divisible by $4$ .

In $27720$ , the digits in ten's and unit's place are $2$ and $0$ , so the number made by these two digits is $20$ . Since $20$ is divisible by $4$ , $27720$ will also be divisible by $4$ .

Divisibility rule of $8$ : If the number made by unit's, ten's and hundredth places is divisible by $8$ , or the number contains $0$ in all these places, then the number would be divisible by $8$ .

In $27720$ the number made by unit's, ten's and hundredth places is $720$ . Since, $720$ is divisible by $8$ , $27720$ will also be divisible by $8$ .

Divisibility rule of $7$ : Take a number and double its last digit. Now subtract this doubled number from the rest of the digits of the original number.
Repeat the process till the result is a digit like $1$ or $2$ . If the obtained number is divisible by $7$ , then the original number also be divisible by $7$ .

In $27720$ , the last digit is $0$ , twice of $0$ is $0$ .

$2772 - 0 = 2772$

In $2772$ , the last digit is $2$ , twice of $2$ is $4$ .

$277 - 4 = 273$

In $273$ , the last digit is $3$ , twice of $3$ is $6$ .

$27 - 6 = 21$

In $21$ , the last digit is $1$ , twice of $2$ is $2$ .

$2 - 2 = 0$

Therefore, $27720$ is divisible by $7$ .

Divisibility rule of $11$ : For any number find out the sum of the digits in the odd places and the sum of the digits in the even places. If the difference between the sum of digits at odd places and places and the sum of digits in even places are $0, 11$ or multiple of $11$ , then the number would be divisible by $11$ .

In $27720$ , the sum of digits in odd places $= 2 + 7 + 0 = 9$ and the sum of digits in even places $= 7 + 2 = 9$

The difference between the two sums: $9 - 9 = 0$

Therefore, $27720$ is divisible by $11$ .

Therefore, the number $27720$ is divisible by $2, 3, 4, 5, 6, 7, 8, 9, 10$ and $11$ .

By which number is $27720$ divisible?

Important Questions on Factors and Multiples

Learn and Prepare for any exam you want !

By which number is 27720 divisible?

Important Questions on Factors and Multiples

Learn and Prepare for any exam you want !

By which number is $27720$ divisible?