Maths-
General
Easy
Question
The remainder of 2100 when divided by 7 is
- 1
- 2
- 3
- 4
Hint:
We have to divide 2100 by 7. We have to find the remainder. We will use the method of congruence.
The correct answer is: 3
We have to find the remainder when 2100 is divided by 7.
We will use the method of congruence to solve the question.
When a is the dividend, b is the remainder and n is the divisor, we can write it in the following form.
a = b(modn)
We will find the value of the dividend in such a way that, we get a remainder 1. Then using that, we can adjust the values we want.
In this question, a = 2100
n = 7
We have to find b.
We will start with a simpler base till we get the remainder 1.
2 = 2(mod7) ...{ 2 divided or modulo by 7 gives us remainder 2}
22 = 4(mod7) ...{ 22 means 4. And, 4 divided by 7 gives us remainder 4}
23 = 1(mod7). ...{23 means 8. And, 8 divided by 7 gives us remainder 1}
We will use this as our base.
299 = (23)33
(23)33 = (1)33 (mod7) = 1(mod7)
We will multiply both the sides by 2.
299 × 2 = 1 × 2(mod7)
2100 = 2(mod7)
So, the remainder of 2100 divided by 7 is 2.
For such questions, we should know the rules of indices.
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