Remainders Basics - 1 | Algebra - Number Theory
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Answer the next 10 questions based on the information given below:
Find the remainder when 85673 is divided by
2
Answer: 1
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Explanation :
To find the remainder of a number when divided by 2, find the remainder of last digits when divided by 2.
∴ The required answer = R[3/2] = 1.
Hence, 1.
Workspace:
4
Answer: 1
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Explanation :
Since 4 = 22.
To find the remainder of a number when divided by 4, find the remainder of last 2 digits when divided by 4.
∴ The required answer = R[73/4] = 1.
Hence, 1.
Workspace:
8
Answer: 1
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Explanation :
Since 8 = 23.
To find the remainder of a number when divided by 4, find the remainder of last 3 digits when divided by 8.
∴ The required answer = R[673/8] = 1.
Hence, 1.
Workspace:
3
Answer: 2
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Explanation :
To find the remainder of a number when divided by 3, find the remainder when sum of the digits is divided by 3.
∴ The required answer = R[(8 + 5 + 6 + 7 + 3)/3] = R[29/3] = 2.
Hence, 2.
Workspace:
9
Answer: 2
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Explanation :
To find the remainder of a number when divided by 9, find the remainder when sum of the digits is divided by 9.
∴ The required answer = R[(8 + 5 + 6 + 7 + 3)/9] = R[29/9] = 2.
Hence, 2.
Workspace:
27
Answer: 2
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Explanation :
To find the remainder of a number when divided by 27, form pairs of 3 digits starting from the right and add all these pairs. Remainder of this sum when divided by 27 is same as the remainder of the number when divided by 27.
∴ The required answer = R[(85 + 673)/27] = R[758/27] = 2.
Hence, 2.
Workspace:
5
Answer: 3
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Explanation :
To find the remainder of a number when divided by 5, find the remainder of last digit when divided by 5.
∴ The required answer = R[3/5] = 3.
Hence, 3.
Workspace:
25
Answer: 23
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Explanation :
Since 25 = 52.
To find the remainder of a number when divided by 5, find the remainder of last 2 digits when divided by 25.
∴ The required answer = R[73/25] = 23.
Hence, 23.
Workspace:
50
Answer: 23
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Explanation :
To find the remainder of a number when divided by 5, find the remainder of last 2 digits when divided by 50.
∴ The required answer = R[73/50] = 23.
Hence, 23.
Workspace:
11
Answer: 5
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Explanation :
To find the remainder of a number when divided by 11.
Let the sum of the alternate digits starting from unit’s digit = U
Let the sum of the alternate digits starting from ten’s digit = T
Remainder of (U - T) when divided by 11 is same as the remainder of the number when divided by 11.
Here, U = 3 + 6 + 8 = 17 and T = 7 + 5 = 12
∴ The required answer = R[(17 - 12)/11] = 5
Hence, 5.
Workspace:
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