Question

What is the last digit of the number 1458793^60 ? i.e. 3 to the power 60

3, 7, 9 or 1?

Answer 1

Hey mate here your ans

${1458793}^{60} \\ unit \: digit \: of \: 3 \: is \\ {3}^{4} = 1 ...(3 \times 3 \times 3 \times 3 = 81) \\ then \: {3}^{6} = 1 \times 3 \times 3 \times = 9 \\ therefore \: we \: got \: unit \: digit \: of \: 3 \: is9$

I hope this will help u

Answer 2

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Answer:

1

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Explanation of the concept used:

As an example, we have to consider a number ending in digit 3 like 3, 13, 23, 33, etc. For getting it simply, consider the number 3.

The unit digit of 3^1 = 3 is 3.

The unit digit of 3^2 = 3 × 3 = 9 is 9.

The unit digit of 3^3 = 9 × 3 = 27 is 7.

(For next step, the unit digit 7 can only be considered instead of 27.)

The unit digit of 7 × 3 = 21 is 1.

By considering the unit digit 1,

The unit digit of 1 × 3 = 3 is 3.

Here the digits are repeated in the same sequence.

So, we can say that,

The 4 possible digits at unit place of 3^n are '3, 9, 7 and 1' ordered, for positive integers n.

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Step-by-step explanation:

=> As the no. of possible digits at unit place of the powers of 3 is 4, divide the exponent 60 by 4 and identity the remainder.

=> In the sequence 3, 9, 7, 1,

• if the remainder on dividing 60 by 4 is 1, then the first number of the sequence is the answer.
• if the remainder on dividing 60 by 4 is 2, then the second number of the sequence is the answer.
• if the remainder on dividing 60 by 4 is 3, then the third number of the sequence is the answer.
• if the remainder on dividing 60 by 4 is 0, then the last number (fourth one) of the sequence is the answer.

=> 60 leaves remainder 0 on division by 4.

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Conclusion:

As the remainder is 0, the last number of the sequence, i.e., 1 is the answer.

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