Question

How many three digit numbers are divisible by 87

Answer 1

$\textbf {Hey there, here is the solution.}$

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Find the smallest 3-digit number that can be divided by 87:

100 ÷ 87 = 1 reminder 13

87 - 13 = 74

100 + 74 = 174

Smallest 3-digit number that can be divided by 87 = 174

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Find the biggest number that can be divided by 87:

1000 ÷ 87 = 11 remainder 3

87 x 11 - 957

Biggest 3-digit number that can be divided by 87 = 957

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Define the AP:

AP Series : 174, 261 .... 957

First term = a1 = 174

difference = d = 87

nth term = an = 957

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Find the number of terms, n:

an = a1 + (n - 1)d

957 = 174 + (n - 1)(87)

957 = 174 + 87n - 87

87n = 870

n = 10

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Answer: There are 10 numbers that are divisible by 87.

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⭐$\textbf {Cheers @ Simmisai}$⭐