Question

Which one of the following numbers will completely divide (5^51 + 5^52 + 5^53 + 5^54 + 5^55 )? *
a) 7
b) 11
c) 9
d) 13​

Answer 1

Answer:

B 11

explanation:

write down

Answer 2

Solution :-

→ (5⁵¹ + 5⁵² + 5⁵³ + 5⁵⁴ + 5⁵⁵)

taking 5⁵¹ common,

→ 5⁵¹(1 + 5 + 5² + 5³ + 5⁴)

→ 5⁵¹(1 + 5 + 25 + 125 + 625)

→ (5⁵¹ * 781)

now,

→ 781 ÷ 7 = Remainder 4

→ 781 ÷ 11 = Remainder 0

→ 781 ÷ 9 = Remainder 7

→ 781 ÷ 13 = Remainder 1

since, when 781 is divided by 11 it gives remainder 0 .

therefore, we can conclude that, (5⁵¹ * 781) is completely divisible by 11 .

Hence, Option (b) 11 is correct answer .

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