Question

When 2 to the power 35 is divided by 5 the remainder is?

Answer 1

2^35=34,359,738,368
divide by 5 is
quotient =6871947673
remainder=3

the remainder is three.

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Answer 2

When 2 to the power 35 is divided by 5 the remainder is 3

2³⁵

= 2³²⁺³

= 2³²×2³

= (2⁴)⁸×2³

= (16)⁸×8

= (15 + 1)⁸×(5 + 3)

= (5 * 3 + 1)⁸×(5 + 3)

(5 * 3 + 1)⁸ divided by 5 will give remainder 1

(5 + 3) divided by 5 will give remainder 3

Remainder = 1×3 = 3

Hence When 2 to the power 35 is divided by 5 the remainder is 3