Question

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What's the last digit of 7^500

Answer 1

Answer:

1

Step-by-step explanation:

Cyclic chart of 7 is:

7¹ = 7

7² = 49

7³ = 343

7⁴ = 2401

7⁵ = 16807

7⁶ = 117649.

From the above it is clear that cyclicity of 7 is 4. Now, with the cyclicity number i.e 4 divide the given number i.e 500. The remainder obtained is 0.

Thus, the last digit of 7⁵⁰⁰ is equal to the last digit of 7⁰ i.e 1.

Therefore, last digit of 7⁵⁰⁰ = 1.

Hope it helps!

Answer 2

Solution :-


7^4 ≡ 1 ( mod 100 )


⇒ 500 = 125 × 4


7^500 ≡ 7^125 × 4 ( mod 100 )


7^500 ≡ (7^4)^125 ( mod 100 )


7^500 ≡ (1)^125 ( mod 100 )


7^500 ≡ 1 ( mod 100 )


∴ The last digit of 7^500 = 1