The given statement is true or false:

25110 is divisible by 45 .

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The given statement is true.
Concept- If the divisor is divided into its components, figuring out if a dividend is divisible is simple. The math that results from trying to determine if 45 is divisible on its own might be challenging. Therefore, it is suggested to divide 45 into its main components.
Here, we must determine whether 25110 may be divided by 45.
The prime factors of a divisor make it simple to compute its divisibility, hence the prime factors of divisor 45 are

Thus, prime factors of 45 are:

(1)
If the total of all the dividend digits is divisible by 3 or less, then the entire dividend is said to be divisible by 3; otherwise, it is not.

(2)
Similar to the 0 or 5 criterion, the dividend is said to be divisible by 5 if the final digit of the dividend is either 0 or 5.

Combining equations (2) and (3), we see that a dividend is only deemed to be 45-divisible if it is also divisible by both 3 and 5.
Consequently, by using the rule of three divisibility on 25110 from equation (2), we obtain

, which is divisible by 3
And applying divisibility rule of 5 from equation (3), we get

last digit is 0 , hence it is also divisible by 5
Thus, we can say that 25110 is divisible by 3 and 5 .
So, 25110 is divisible by 45 .
Hence, the given statement is true.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th