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If 22006 - 2006 divided by 7, the remainder is
- a)0
- b)1
- c)2
- d)4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If 22006 - 2006 divided by 7, the remainder isa)0b)1c)2d)4Correct answ...
Problem:
Find the remainder when 22006 - 2006 is divided by 7.
Solution:
To find the remainder when a number is divided by another number, we can use the concept of congruence. Two numbers are said to be congruent modulo n if their difference is divisible by n.
Let's represent the given expression as a congruence equation:
22006 - 2006 ≡ x (mod 7)
Step 1: Simplify the expression on the left side of the congruence equation.
22006 - 2006 = 20000
The congruence equation becomes:
20000 ≡ x (mod 7)
Step 2: Find the remainder when 20000 is divided by 7.
To find the remainder, we divide 20000 by 7 and observe the remainder.
20000 ÷ 7 = 2857 remainder 1
Therefore, 20000 leaves a remainder of 1 when divided by 7.
Step 3: Substitute the remainder in the congruence equation.
x ≡ 1 (mod 7)
Answer:
The remainder when 22006 - 2006 is divided by 7 is 1. Therefore, option 'A' is the correct answer.
Find the remainder when 22006 - 2006 is divided by 7.
Solution:
To find the remainder when a number is divided by another number, we can use the concept of congruence. Two numbers are said to be congruent modulo n if their difference is divisible by n.
Let's represent the given expression as a congruence equation:
22006 - 2006 ≡ x (mod 7)
Step 1: Simplify the expression on the left side of the congruence equation.
22006 - 2006 = 20000
The congruence equation becomes:
20000 ≡ x (mod 7)
Step 2: Find the remainder when 20000 is divided by 7.
To find the remainder, we divide 20000 by 7 and observe the remainder.
20000 ÷ 7 = 2857 remainder 1
Therefore, 20000 leaves a remainder of 1 when divided by 7.
Step 3: Substitute the remainder in the congruence equation.
x ≡ 1 (mod 7)
Answer:
The remainder when 22006 - 2006 is divided by 7 is 1. Therefore, option 'A' is the correct answer.
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Community Answer
If 22006 - 2006 divided by 7, the remainder isa)0b)1c)2d)4Correct answ...
22006 = 4(8)668 = 4 (7 +1)668 leaves remainder 4
2006 = 7 x 268 + 4 leaves remainder
∴ 22006 - 2006 leaves remainder 0.
2006 = 7 x 268 + 4 leaves remainder
∴ 22006 - 2006 leaves remainder 0.
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