Question

Find the smallest five-digit number which is exactly divisible by 273 step by step explanation ​

Answer 1

I hope this help

thankyou

Answer 2

Answer:

As we know the smallest five-digit number is 10000. And here, we need to determine the smallest five-digit number which is exactly divisible by 273.

Now, we know the number divisible by 273 must be higher than 100,00 or equals to it.So, if we divide the number 100,00 by 273, we will get some value of remainder and if we subtract that remainder from 100,00 the number found will be divisible by 273 as per the rules of division of numbers. And hence if we add 273 to that number we will get a number with five digits and that will be divisible by 273 as well because we will not get the remainder higher than 273 if we divide 10000 by 273;So,let us understand the above approach with applying it as well.

So, divide 100,00 by 273 in following ways

Now, we know that the value of remainder is 172.So, if we subtract 172 from 100,00, we will get a number which will be exactly divisible by 273.So we get number as

Number divisible by 273 = 100,00 – 172

= 9828

But the number 9828 is the four-digit number, which is divisible by 273.But as we need to determine the five-digit number which will be divisible by 273.So, we can get just next multiple of 273 by just adding 273 to the number 9828.So, we get

Number with 5-digit divisible by 273 = 273 + 9828

= 10101

Hence, 10101 is the least five-digit number which will be divisible by 273

Note: One may get confused with the statement that if 10000 will be subtracted to the remainder, then how the calculated number will be multiple of 273.So, let us look at the Euclid’s division lemma, which can be given as

a = bq + r

where, we are dividing number ‘a’ and ‘b’ and got quotient as ‘q’ and remainder ‘r’

So, we can rewrite the above expression as

a – r = bq

Now, we can observe that a – r is the multiplication of b and q, it means (a – r) is a multiple of ‘b’ by

‘q’ times. Hence, 10000

hope you like it