Question

What is the remainder of 3^2019 when divided by 10?​

Answer 1

Solution :-

We know that,

• When any number is divided by 10, the remainder we gets is the unit digit of the number which is divided .
• Ex. :- 52 ÷ 10 = 2 remainder , 987 ÷ 10 = 7 remainder , 56784 ÷ 10 = 4 remainder .

So,

→ 3²⁰¹⁹ ÷ 10 = Unit digit 3²⁰¹⁹

then,

→ 3²⁰¹⁹

→ 3^(2016 + 3)

→ 3²⁰¹⁶ * 3³

→ 3^(4 * 504) * 3³

→ (3⁴)⁵⁰⁴ * 3³

→ (81)⁵⁰⁴ * 3³

→ 1 * 27

→ 7 unit digit .

therefore, the remainder of 3²⁰¹⁹ when divided by 10 is equal to 7 .

Learn more :-

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Answer 2

Answer:

The remainder will be 7.

Step-by-step explanation:

As per the data given in the question,

We know that reminder of a number divisible by 10 is the last digit of a number.

Like, 54648/10 will give remainder 8.

So, we just need to find out last digit of $3^{2019}$

$=3^{2019} \\=3^{2016+3}\\=3^{2016}\times 3^{23} \\=3^{4\times504}\times 3^{3} \\=(3^{4})^{504} \times3^{3}\\=81^{504}\times3^{3}\\As\:power\:of 81\:will\:always\:end\:with\:1\\=1\times27\\=7\:at\:unit\:digit$

As, 7 is the last digit, so, remainder will be 7.

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