What Are The Multiples Of 25 And How To Find Them
Understanding the Multiples of 25 is a key part of arithmetic and number theory that helps students solve problems involving grouping, currency calculations, and division. Knowing how to list and use multiples of 25 is useful for school exams, competitive tests, and everyday maths challenges.
Understanding Multiples of 25
A multiple of 25 is any number you get by multiplying 25 by a whole number (integer). In other words, if you can write a number as \( 25 \times n \) where \( n \) is a whole number (0, 1, 2, 3, ...), then that number is a multiple of 25. For example, 50, 125, and 250 are all multiples of 25 because:
- 25 × 2 = 50
- 25 × 5 = 125
- 25 × 10 = 250
Multiples of 25 are common in topics such as times tables, number patterns, grouping objects equally, and checking divisibility in maths.
Formula to Find Multiples of 25
To find any multiple of 25, use this formula:
Multiple = 25 × n (where n is any whole number)
For example, to find the 8th multiple of 25:
25 × 8 = 200
So, 200 is the 8th multiple of 25.
List of Multiples of 25 (Up to 1000)
Here are the first 40 multiples of 25. You can use this as a quick reference for homework, assignments, or competitive exams:
| n | 25 × n | Multiple | n | 25 × n | Multiple |
|---|---|---|---|---|---|
| 1 | 25 × 1 | 25 | 21 | 25 × 21 | 525 |
| 2 | 25 × 2 | 50 | 22 | 25 × 22 | 550 |
| 3 | 25 × 3 | 75 | 23 | 25 × 23 | 575 |
| 4 | 25 × 4 | 100 | 24 | 25 × 24 | 600 |
| 5 | 25 × 5 | 125 | 25 | 25 × 25 | 625 |
| 6 | 25 × 6 | 150 | 26 | 25 × 26 | 650 |
| 7 | 25 × 7 | 175 | 27 | 25 × 27 | 675 |
| 8 | 25 × 8 | 200 | 28 | 25 × 28 | 700 |
| 9 | 25 × 9 | 225 | 29 | 25 × 29 | 725 |
| 10 | 25 × 10 | 250 | 30 | 25 × 30 | 750 |
| 11 | 25 × 11 | 275 | 31 | 25 × 31 | 775 |
| 12 | 25 × 12 | 300 | 32 | 25 × 32 | 800 |
| 13 | 25 × 13 | 325 | 33 | 25 × 33 | 825 |
| 14 | 25 × 14 | 350 | 34 | 25 × 34 | 850 |
| 15 | 25 × 15 | 375 | 35 | 25 × 35 | 875 |
| 16 | 25 × 16 | 400 | 36 | 25 × 36 | 900 |
| 17 | 25 × 17 | 425 | 37 | 25 × 37 | 925 |
| 18 | 25 × 18 | 450 | 38 | 25 × 38 | 950 |
| 19 | 25 × 19 | 475 | 39 | 25 × 39 | 975 |
| 20 | 25 × 20 | 500 | 40 | 25 × 40 | 1000 |
Number Patterns and Tips to Recognise Multiples of 25
- Every multiple of 25 ends with 00, 25, 50, or 75.
- The difference between any two consecutive multiples of 25 is always 25. (Example: 200 → 225 → 250)
- Multiples of 100 (like 100, 200, 300, 400...) are always multiples of 25 too.
- If a number divides evenly by 25 (no remainder), then it is a multiple of 25.
Recognising these patterns will help you spot multiples of 25 quickly in exams and daily life.
Comparison: Multiples of 24, 25, and 50
| 1st Few Multiples of 24 | 1st Few Multiples of 25 | 1st Few Multiples of 50 |
|---|---|---|
| 24, 48, 72, 96, 120, 144 | 25, 50, 75, 100, 125, 150 | 50, 100, 150, 200, 250, 300 |
You can see that some numbers (like 100, 150, 200, 300, etc.) are common multiples for all three. Notice especially that every multiple of 50 is also a multiple of 25.
Worked Examples: Multiples of 25 in Practice
Example 1: Is 525 a multiple of 25?
- Divide 525 by 25: 525 ÷ 25 = 21
- 21 is a whole number, so 525 is a multiple of 25.
Example 2: Find the 30th multiple of 25.
- Use the formula: 25 × 30 = 750
- The 30th multiple is 750.
Example 3: If a box holds 25 chocolates, how many boxes are needed for 600 chocolates?
- 600 ÷ 25 = 24
- So, 24 boxes exactly are needed.
Practice Problems
- List the first 10 multiples of 25.
- Check whether 875 is a multiple of 25.
- Find the smallest multiple of 25 that is greater than 320.
- How many multiples of 25 are there between 100 and 300?
- Is 1000 a multiple of both 25 and 50?
Common Mistakes to Avoid
- Confusing multiples with factors. Remember, multiples of 25 are numbers you get when you multiply 25 by whole numbers (e.g. 25, 50, 75), NOT the numbers that divide 25 (1, 5, 25).
- Forgetting that some multiples of 25 are odd (e.g., 75, 125). Not all multiples are even.
- Thinking only numbers ending with zero are multiples of 25. Numbers ending with 25, 50, or 75 are also multiples.
Real-World Applications
Multiples of 25 are used every day, especially in:
- Currency: Coins and notes are often valued in multiples of 25.
- Time: A quarter-hour is 15 minutes, but things like quarters in sports and academic scoring often use multiples of 25 or 100.
- Packing/Grouping: Distributing items into equal sets, such as 25 students in a class or 25 items in a pack.
A quick trick: To multiply a number by 25, multiply it by 100 and then divide by 4. For example, 16 × 25 = (16 × 100) ÷ 4 = 1600 ÷ 4 = 400.
At Vedantu, we make these shortcuts and applications simple to understand so you can use them with speed in exams and everyday maths.
You can also explore the Table of 25 and Factors of 25 pages for deeper learning.
In this topic, we learned about Multiples of 25, how to find them, recognize their patterns, and use them for division and real-world problems. Practicing this concept with tables and problems helps you master number theory and prepares you for faster calculations in all maths exams.
FAQs on Multiples Of 25 Explained With Patterns And Examples
1. What are multiples of 25?
Multiples of 25 are numbers that you get when you multiply 25 by any whole number. In other words, a multiple of 25 is of the form 25 × n, where n is a whole number.
- 25 × 1 = 25
- 25 × 2 = 50
- 25 × 3 = 75
- 25 × 4 = 100
2. How do you find multiples of 25?
To find multiples of 25, multiply 25 by whole numbers like 1, 2, 3, and so on. The formula is 25 × n, where n is a whole number.
- 25 × 5 = 125
- 25 × 8 = 200
- 25 × 12 = 300
3. What are the first 10 multiples of 25?
The first 10 multiples of 25 are obtained by multiplying 25 by numbers from 1 to 10.
- 25 × 1 = 25
- 25 × 2 = 50
- 25 × 3 = 75
- 25 × 4 = 100
- 25 × 5 = 125
- 25 × 6 = 150
- 25 × 7 = 175
- 25 × 8 = 200
- 25 × 9 = 225
- 25 × 10 = 250
4. What is the rule for multiples of 25?
A number is a multiple of 25 if it ends in 00, 25, 50, or 75. This works because 25 × 4 = 100, so multiples repeat in a pattern of four in the last two digits.
- 25 → ends in 25
- 50 → ends in 50
- 75 → ends in 75
- 100 → ends in 00
5. How do you check if a number is divisible by 25?
A number is divisible by 25 if its last two digits are 00, 25, 50, or 75. This is the divisibility rule for 25.
- 225 → ends in 25 ✅
- 450 → ends in 50 ✅
- 310 → ends in 10 ❌
6. Why do multiples of 25 end in 00, 25, 50, or 75?
Multiples of 25 end in 00, 25, 50, or 75 because 25 × 4 = 100, which creates a repeating pattern in the last two digits. Every four multiples increase by 100.
- 25 × 1 = 25
- 25 × 2 = 50
- 25 × 3 = 75
- 25 × 4 = 100
7. What is the smallest and largest multiple of 25?
The smallest positive multiple of 25 is 25, and there is no largest multiple because multiples continue infinitely. Since you can keep multiplying 25 by larger whole numbers, the list never ends.
- Smallest positive multiple: 25 × 1 = 25
- No largest multiple (infinite sequence)
8. Are all multiples of 25 also multiples of 5?
Yes, all multiples of 25 are also multiples of 5 because 25 itself is divisible by 5. Since 25 = 5 × 5, any number of the form 25 × n will also contain a factor of 5.
- 25 = 5 × 5
- 50 = 5 × 10
- 75 = 5 × 15
9. What is the formula to find the nth multiple of 25?
The formula to find the nth multiple of 25 is 25n, where n is a natural number. This gives the exact value of any position in the sequence.
- 1st multiple: 25 × 1 = 25
- 5th multiple: 25 × 5 = 125
- 12th multiple: 25 × 12 = 300
10. What is the difference between factors and multiples of 25?
The difference is that factors of 25 divide 25 exactly, while multiples of 25 are numbers obtained by multiplying 25 by whole numbers. Factors are limited, but multiples continue infinitely.
- Factors of 25: 1, 5, 25
- Multiples of 25: 25, 50, 75, 100, 125, …
