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What is the remainder of 7^406 when divided by 11?

1 Answer

4 votes

Answer:36
10 remainder

Explanation:

Step 1:

Start by setting it up with the divisor 11 on the left side and the dividend 406 on the right side like this:

1 1 ⟌ 4 0 6

Step 2:

The divisor (11) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

0

1 1 ⟌ 4 0 6

Step 3:

Multiply the divisor by the result in the previous step (11 x 0 = 0) and write that answer below the dividend.

0

1 1 ⟌ 4 0 6

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.

0

1 1 ⟌ 4 0 6

- 0

4

Step 5:

Move down the 2nd digit of the dividend (0) like this:

0

1 1 ⟌ 4 0 6

- 0

4 0

Step 6:

The divisor (11) goes into the bottom number (40), 3 times (s). Therefore, put 3 on top:

0 3

1 1 ⟌ 4 0 6

- 0

4 0

Step 7:

Multiply the divisor by the result in the previous step (11 x 3 = 33) and write that answer at the bottom:

0 3

1 1 ⟌ 4 0 6

- 0

4 0

3 3

Step 8:

Subtract the result in the previous step from the number written above it. (40 - 33 = 7) and write the answer at the bottom.

0 3

1 1 ⟌ 4 0 6

- 0

4 0

- 3 3

7

Step 9:

Move down the last digit of the dividend (6) like this:

0 3

1 1 ⟌ 4 0 6

- 0

4 0

- 3 3

7 6

Step 10:

The divisor (11) goes into the bottom number (76), 6 time(s). Therefore put 6 on top:

0 3 6

1 1 ⟌ 4 0 6

- 0

4 0

- 3 3

7 6

Step 11:

Multiply the divisor by the result in the previous step (11 x 6 = 66) and write the answer at the bottom:

0 3 6

1 1 ⟌ 4 0 6

- 0

4 0

- 3 3

7 6

6 6

Step 12:

Subtract the result in the previous step from the number written above it. (76 - 66 = 10) and write the answer at the bottom.

0 3 6

1 1 ⟌ 4 0 6

- 0

4 0

- 3 3

7 6

- 6 6

1 0

You are done because there are no more digits to move down from the dividend.

÷

User Ababneh A
by
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