Last updated on July 5th, 2025
The leftover value after division is referred to as the remainder. When the given number doesn’t get divided evenly, the leftover value will be taken as the remainder. The remainder is what’s left over when objects are divided into equal groups. A remainder will always be less than the divisor. For example, 17 cookies are being shared equally among 5 children. Here, we divide 17 by 5 to find out how much each gets and how many are remaining. So, each child gets 3 cookies, and 2 cookies remain.
The leftover value after division is referred to as the remainder. When the given number doesn’t get divided evenly, the leftover value will be taken as the remainder. The remainder is what’s left over when objects are divided into equal groups. A remainder will always be less than the divisor.
For example, 17 cookies are being shared equally among 5 children. Here, we divide 17 by 5 to find out how much each gets and how many are remaining. So, each child gets 3 cookies, and 2 cookies remain.
In math, we can represent the remainder of a division in two ways:
Long division is the best method to find the remainder, especially when dealing with large numbers. It breaks the problem into smaller, easy-to-follow steps.
Example: Divide 47 by 5 using long division
Understanding the concept of remainders helps students solve division problems that do not result in whole numbers. However, errors can happen while they are dealing with remainders. Here are some common mistakes and useful ways to avoid them:
Remainders help us understand and deal with situations where division doesn’t result in a whole number. They frequently emerge in real-world situations where items cannot be distributed evenly. Here are some practical applications of remainders:
Sharing things: When dividing a set number of objects (such as cookies, pencils, or books) among a group, the remainder indicates how many items remain after everyone has received an equal part.
Budgeting and Resource Allocation: When a budget or resources are divided equally among departments or people, the remainder shows what’s left over. This leftover amount may be allocated or handled separately.
Time Calculations: When time is divided into intervals, such as hours into minutes or days into weeks, the remainder can be used to calculate how much time remains after counting full units.
What is the remainder when 5 × 6 × 7 is divided by 4?
2
First, calculate the product: 5 × 6 × 7 = 210. Now divide by 4: 210 ÷ 4 = 52 remainder 2.
What is the remainder when 4327 is divided by 23? Check if the answer you got is correct.
3
Divide 4327 by 23: 23 goes into 43 1 time → 1 × 23 = 23
43 – 23 = 20
Bring down the next digit → 2 → Now we have 202. 23 goes into 202 8 times → 8 × 23 = 184
202–184 = 18
Bring down the next digit → 7 → Now we have 187. 23 goes into 187 8 times → 8 × 23 = 184
187–184 = 3.
Therefore, the quotient is 188, and the remainder is 3.
The number of days in the year 2000 was 366, as it was a leap year. If 1st Jan 2000 was a Saturday, what day was it on 1st Jan 2001?
1st January 2001 was a Monday.
We want to find the remainder: 366 ÷ 7 = 52 weeks + remainder 2.
Then, add the remainder to the given day. 1st Jan 2000 was a Saturday.
Now, add 2 days to Saturday:
Saturday + 1 day = Sunday
Sunday + 1 day = Monday
It is given that 1st Jan 2000 was a Saturday.
We know that every day of the week repeats exactly after 7 days.
Since 2000 is a leap year, it has 366 days.
Find the remainder when the sum 25 + 37 + 46 is divided by 8.
4
25 + 37 + 46 = 108
Divide the answer by 8: 108 ÷ 8 = 13 remainder 4.
What is the remainder when 3^4 is divided by 5?
1
Here, 34 = 81.
Therefore, 81 ÷ 5 = 16 remainder 1
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.