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When a number is divided by 63 the remainder is obtained as 26. What will be the remainder when the number is divided by 3?
- a)1
- b)2
- c)3
- d)5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
When a number is divided by 63 the remainder is obtained as 26. What w...
Let x and q be the number and quotient respectively so, we can write
⇒ x = 63q + 26
⇒ x = (3 × 21q) + (3 × 8) + 2
⇒ x = 3(21q + 8) + 2
∴ When the number is divided by 3, the remainder is 2
⇒ x = 63q + 26
⇒ x = (3 × 21q) + (3 × 8) + 2
⇒ x = 3(21q + 8) + 2
∴ When the number is divided by 3, the remainder is 2
Most Upvoted Answer
When a number is divided by 63 the remainder is obtained as 26. What w...
To find the remainder when a number is divided by 3, we need to understand the pattern of remainders when dividing by 3.
The remainder when any number is divided by 3 will be one of three possible values: 0, 1, or 2.
Let's consider the given information: when the number is divided by 63, the remainder is 26.
We can express this as an equation: number = 63a + 26, where 'a' is an integer.
To find the remainder when the number is divided by 3, we need to simplify the equation.
Let's divide both sides of the equation by 3:
number/3 = (63a + 26)/3
Simplifying further, we get:
number/3 = 21a + 8 + 2/3
Since 'a' is an integer, 21a is divisible by 3. So we can ignore it for finding the remainder.
Now, let's focus on the remaining terms: 8 + 2/3.
As per the pattern of remainders when dividing by 3, we can see that the remainder of 8 when divided by 3 is 2. Moreover, the remainder of 2/3 when divided by 3 is 2.
Thus, the remainder when the number is divided by 3 is the sum of these remainders, which is 2 + 2 = 4.
However, since the remainder must be less than the divisor (3 in this case), we need to find the remainder of 4 when divided by 3.
The remainder when 4 is divided by 3 is 1.
Therefore, the correct answer is option B) 2.
The remainder when any number is divided by 3 will be one of three possible values: 0, 1, or 2.
Let's consider the given information: when the number is divided by 63, the remainder is 26.
We can express this as an equation: number = 63a + 26, where 'a' is an integer.
To find the remainder when the number is divided by 3, we need to simplify the equation.
Let's divide both sides of the equation by 3:
number/3 = (63a + 26)/3
Simplifying further, we get:
number/3 = 21a + 8 + 2/3
Since 'a' is an integer, 21a is divisible by 3. So we can ignore it for finding the remainder.
Now, let's focus on the remaining terms: 8 + 2/3.
As per the pattern of remainders when dividing by 3, we can see that the remainder of 8 when divided by 3 is 2. Moreover, the remainder of 2/3 when divided by 3 is 2.
Thus, the remainder when the number is divided by 3 is the sum of these remainders, which is 2 + 2 = 4.
However, since the remainder must be less than the divisor (3 in this case), we need to find the remainder of 4 when divided by 3.
The remainder when 4 is divided by 3 is 1.
Therefore, the correct answer is option B) 2.
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