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A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, then the remainder is:
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A number divided by 68 gives the quotient 269 and remainder zero. If t...
The number is 68 × 269 = 18292. 18292, when divided by 67, leaves a remainder of 1.
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A number divided by 68 gives the quotient 269 and remainder zero. If t...
To find the remainder when a number is divided by a divisor, we can use the concept of congruence. Two numbers are said to be congruent modulo a divisor if they leave the same remainder when divided by that divisor.
Given information:
Number divided by 68 gives the quotient 269 and remainder zero.
Let's assume the number to be 'N'.
1. Dividing N by 68:
N = 68 * 269 + 0
N ≡ 0 (mod 68)
Now, we need to find the remainder when N is divided by 67.
Using the concept of congruence, we can write:
N ≡ 0 (mod 68)
This means N is congruent to 0 modulo 68.
We can rewrite this congruence as:
N ≡ 0 + (67 * 1) (mod 68)
N ≡ 67 (mod 68)
This implies that N leaves a remainder of 67 when divided by 68.
To find the remainder when N is divided by 67, we need to find the congruence of N modulo 67.
N ≡ 67 (mod 68)
We can rewrite this congruence as:
N ≡ 67 + (67 * 1) (mod 68)
N ≡ 134 (mod 68)
N ≡ 66 (mod 68)
This implies that N leaves a remainder of 66 when divided by 68.
Therefore, the correct answer is option 'B': 1.
Given information:
Number divided by 68 gives the quotient 269 and remainder zero.
Let's assume the number to be 'N'.
1. Dividing N by 68:
N = 68 * 269 + 0
N ≡ 0 (mod 68)
Now, we need to find the remainder when N is divided by 67.
Using the concept of congruence, we can write:
N ≡ 0 (mod 68)
This means N is congruent to 0 modulo 68.
We can rewrite this congruence as:
N ≡ 0 + (67 * 1) (mod 68)
N ≡ 67 (mod 68)
This implies that N leaves a remainder of 67 when divided by 68.
To find the remainder when N is divided by 67, we need to find the congruence of N modulo 67.
N ≡ 67 (mod 68)
We can rewrite this congruence as:
N ≡ 67 + (67 * 1) (mod 68)
N ≡ 134 (mod 68)
N ≡ 66 (mod 68)
This implies that N leaves a remainder of 66 when divided by 68.
Therefore, the correct answer is option 'B': 1.
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A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, then the remainder is:a)0b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?
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