Understanding multiples of 36 involves recognizing how this integer interacts with other numbers through multiplication. Multiples of 36 are numbers that can be expressed as 36 times another whole number. In mathematics, these multiples can also be viewed as the result of multiplying 36 by integers such as 1, 2, 3, and so forth. These values are closely related to the divisors and factors of 36, as any multiple of 36 will inherently share common factors with 36. This concept is essential for exploring broader mathematical principles involving multiples and their applications.
What are Multiples of 36?
Multiples of 36 are the products obtained by multiplying 36 by any integer. Examples include 36, 72, 108, 144, and so on. These numbers follow the pattern 36n, where n is any integer.
For example, 144, 216, 252 and 324 are all multiples of 36, 353 is not a multiple of 36 for the following reasons:
| Number | Calculation | Reason | Remainder |
|---|---|---|---|
| 144 | 144÷36 = 4 | 144 is a multiple of 36 because it divides evenly. | 0 |
| 216 | 216÷36 = 6 | 216 is a multiple of 36 because it divides evenly. | 0 |
| 252 | 252÷36 = 7 | 252 is a multiple of 36 because it divides evenly. | 0 |
| 324 | 324÷36 = 9 | 324 is a multiple of 36 because it divides evenly. | 0 |
| 353 | 353÷36 = 9 | 353 is not a multiple of 36 because it does not divide evenly. | 29 |
List of First 100 Multiples of 36 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 36 | 36 is a multiple of 36 because 36 × 1 = 36 | 0 |
| 72 | 72 is a multiple of 36 because 36 × 2 = 72 | 0 |
| 108 | 108 is a multiple of 36 because 36 × 3 = 108 | 0 |
| 144 | 144 is a multiple of 36 because 36 × 4 = 144 | 0 |
| 180 | 180 is a multiple of 36 because 36 × 5 = 180 | 0 |
| 216 | 216 is a multiple of 36 because 36 × 6 = 216 | 0 |
| 252 | 252 is a multiple of 36 because 36 × 7 = 252 | 0 |
| 288 | 288 is a multiple of 36 because 36 × 8 = 288 | 0 |
| 324 | 324 is a multiple of 36 because 36 × 9 = 324 | 0 |
| 360 | 360 is a multiple of 36 because 36 × 10 = 360 | 0 |
| 396 | 396 is a multiple of 36 because 36 × 11 = 396 | 0 |
| 432 | 432 is a multiple of 36 because 36 × 12 = 432 | 0 |
| 468 | 468 is a multiple of 36 because 36 × 13 = 468 | 0 |
| 504 | 504 is a multiple of 36 because 36 × 14 = 504 | 0 |
| 540 | 540 is a multiple of 36 because 36 × 15 = 540 | 0 |
| 576 | 576 is a multiple of 36 because 36 × 16 = 576 | 0 |
| 612 | 612 is a multiple of 36 because 36 × 17 = 612 | 0 |
| 648 | 648 is a multiple of 36 because 36 × 18 = 648 | 0 |
| 684 | 684 is a multiple of 36 because 36 × 19 = 684 | 0 |
| 720 | 720 is a multiple of 36 because 36 × 20 = 720 | 0 |
| 756 | 756 is a multiple of 36 because 36 × 21 = 756 | 0 |
| 792 | 792 is a multiple of 36 because 36 × 22 = 792 | 0 |
| 828 | 828 is a multiple of 36 because 36 × 23 = 828 | 0 |
| 864 | 864 is a multiple of 36 because 36 × 24 = 864 | 0 |
| 900 | 900 is a multiple of 36 because 36 × 25 = 900 | 0 |
| 936 | 936 is a multiple of 36 because 36 × 26 = 936 | 0 |
| 972 | 972 is a multiple of 36 because 36 × 27 = 972 | 0 |
| 1008 | 1008 is a multiple of 36 because 36 × 28 = 1008 | 0 |
| 1044 | 1044 is a multiple of 36 because 36 × 29 = 1044 | 0 |
| 1080 | 1080 is a multiple of 36 because 36 × 30 = 1080 | 0 |
| 1116 | 1116 is a multiple of 36 because 36 × 31 = 1116 | 0 |
| 1152 | 1152 is a multiple of 36 because 36 × 32 = 1152 | 0 |
| 1188 | 1188 is a multiple of 36 because 36 × 33 = 1188 | 0 |
| 1224 | 1224 is a multiple of 36 because 36 × 34 = 1224 | 0 |
| 1260 | 1260 is a multiple of 36 because 36 × 35 = 1260 | 0 |
| 1296 | 1296 is a multiple of 36 because 36 × 36 = 1296 | 0 |
| 1332 | 1332 is a multiple of 36 because 36 × 37 = 1332 | 0 |
| 1368 | 1368 is a multiple of 36 because 36 × 38 = 1368 | 0 |
| 1404 | 1404 is a multiple of 36 because 36 × 39 = 1404 | 0 |
| 1440 | 1440 is a multiple of 36 because 36 × 40 = 1440 | 0 |
| 1476 | 1476 is a multiple of 36 because 36 × 41 = 1476 | 0 |
| 1512 | 1512 is a multiple of 36 because 36 × 42 = 1512 | 0 |
| 1548 | 1548 is a multiple of 36 because 36 × 43 = 1548 | 0 |
| 1584 | 1584 is a multiple of 36 because 36 × 44 = 1584 | 0 |
| 1620 | 1620 is a multiple of 36 because 36 × 45 = 1620 | 0 |
| 1656 | 1656 is a multiple of 36 because 36 × 46 = 1656 | 0 |
| 1692 | 1692 is a multiple of 36 because 36 × 47 = 1692 | 0 |
| 1728 | 1728 is a multiple of 36 because 36 × 48 = 1728 | 0 |
| 1764 | 1764 is a multiple of 36 because 36 × 49 = 1764 | 0 |
| 1800 | 1800 is a multiple of 36 because 36 × 50 = 1800 | 0 |
| 1836 | 1836 is a multiple of 36 because 36 × 51 = 1836 | 0 |
| 1872 | 1872 is a multiple of 36 because 36 × 52 = 1872 | 0 |
| 1908 | 1908 is a multiple of 36 because 36 × 53 = 1908 | 0 |
| 1944 | 1944 is a multiple of 36 because 36 × 54 = 1944 | 0 |
| 1980 | 1980 is a multiple of 36 because 36 × 55 = 1980 | 0 |
| 2016 | 2016 is a multiple of 36 because 36 × 56 = 2016 | 0 |
| 2052 | 2052 is a multiple of 36 because 36 × 57 = 2052 | 0 |
| 2088 | 2088 is a multiple of 36 because 36 × 58 = 2088 | 0 |
| 2124 | 2124 is a multiple of 36 because 36 × 59 = 2124 | 0 |
| 2160 | 2160 is a multiple of 36 because 36 × 60 = 2160 | 0 |
| 2196 | 2196 is a multiple of 36 because 36 × 61 = 2196 | 0 |
| 2232 | 2232 is a multiple of 36 because 36 × 62 = 2232 | 0 |
| 2268 | 2268 is a multiple of 36 because 36 × 63 = 2268 | 0 |
| 2304 | 2304 is a multiple of 36 because 36 × 64 = 2304 | 0 |
| 2340 | 2340 is a multiple of 36 because 36 × 65 = 2340 | 0 |
| 2376 | 2376 is a multiple of 36 because 36 × 66 = 2376 | 0 |
| 2412 | 2412 is a multiple of 36 because 36 × 67 = 2412 | 0 |
| 2448 | 2448 is a multiple of 36 because 36 × 68 = 2448 | 0 |
| 2484 | 2484 is a multiple of 36 because 36 × 69 = 2484 | 0 |
| 2520 | 2520 is a multiple of 36 because 36 × 70 = 2520 | 0 |
| 2556 | 2556 is a multiple of 36 because 36 × 71 = 2556 | 0 |
| 2592 | 2592 is a multiple of 36 because 36 × 72 = 2592 | 0 |
| 2628 | 2628 is a multiple of 36 because 36 × 73 = 2628 | 0 |
| 2664 | 2664 is a multiple of 36 because 36 × 74 = 2664 | 0 |
| 2700 | 2700 is a multiple of 36 because 36 × 75 = 2700 | 0 |
| 2736 | 2736 is a multiple of 36 because 36 × 76 = 2736 | 0 |
| 2772 | 2772 is a multiple of 36 because 36 × 77 = 2772 | 0 |
| 2808 | 2808 is a multiple of 36 because 36 × 78 = 2808 | 0 |
| 2844 | 2844 is a multiple of 36 because 36 × 79 = 2844 | 0 |
| 2880 | 2880 is a multiple of 36 because 36 × 80 = 2880 | 0 |
| 2916 | 2916 is a multiple of 36 because 36 × 81 = 2916 | 0 |
| 2952 | 2952 is a multiple of 36 because 36 × 82 = 2952 | 0 |
| 2988 | 2988 is a multiple of 36 because 36 × 83 = 2988 | 0 |
| 3024 | 3024 is a multiple of 36 because 36 × 84 = 3024 | 0 |
| 3060 | 3060 is a multiple of 36 because 36 × 85 = 3060 | 0 |
| 3096 | 3096 is a multiple of 36 because 36 × 86 = 3096 | 0 |
| 3132 | 3132 is a multiple of 36 because 36 × 87 = 3132 | 0 |
| 3168 | 3168 is a multiple of 36 because 36 × 88 = 3168 | 0 |
| 3204 | 3204 is a multiple of 36 because 36 × 89 = 3204 | 0 |
| 3240 | 3240 is a multiple of 36 because 36 × 90 = 3240 | 0 |
| 3276 | 3276 is a multiple of 36 because 36 × 91 = 3276 | 0 |
| 3312 | 3312 is a multiple of 36 because 36 × 92 = 3312 | 0 |
| 3348 | 3348 is a multiple of 36 because 36 × 93 = 3348 | 0 |
| 3384 | 3384 is a multiple of 36 because 36 × 94 = 3384 | 0 |
| 3420 | 3420 is a multiple of 36 because 36 × 95 = 3420 | 0 |
| 3456 | 3456 is a multiple of 36 because 36 × 96 = 3456 | 0 |
| 3492 | 3492 is a multiple of 36 because 36 × 97 = 3492 | 0 |
| 3528 | 3528 is a multiple of 36 because 36 × 98 = 3528 | 0 |
| 3564 | 3564 is a multiple of 36 because 36 × 99 = 3564 | 0 |
| 3600 | 3600 is a multiple of 36 because 36 × 100 = 3600 | 0 |
Read More About Multiples of 36
Important Notes
Definition: A multiple of 36 is any number that can be expressed as 36 times an integer. For example, 36, 72, 108, etc.
Even Number: Since 36 is an even number, all its multiples are also even numbers.
Divisibility Rules: A number is a multiple of 36 if it is divisible by both 4 and 9, as 36 = 4 × 9. This means the number must pass both the divisibility rules for 4 (last two digits form a number divisible by 4) and 9 (sum of the digits is divisible by 9).
Prime Factorization: The prime factorization of 36 is 2² × 3². Therefore, any multiple of 36 will have at least these prime factors raised to at least these powers.
Common Multiples: To find common multiples of 36 with another number, find the least common multiple (LCM) of 36 and the other number. The LCM is the smallest number that is a multiple of both.
Examples on Multiples of 36
Here are five examples of multiples of 36, presented in a similar structure:
Simple Multiples of 36
- 1×36 = 36
- 2×36 = 72
- 3×36 = 108
Larger Multiples of 36
- 10×36 = 360
- 20×36 = 720
Real-Life Examples of Multiples of 36
- Area Calculation: An area of 144 square meters is a multiple of 36 because 4×36 = 144.
- Storage Capacity: A data storage of 360 GB is a multiple of 36 because 10×36 = 360.
- Inventory: A stock of 720 items is a multiple of 36 because 20×36 = 720.
Practical Examples of Multiples of 36
What is the 5th multiple of 36?
The 5th multiple of 36 is 5×36 = 180.
Is 432 a multiple of 36?
Yes, 432 is a multiple of 36 because 36×12 = 432.
What is the next multiple of 36 after 360?
The next multiple of 36 after 360 is 360+36 = 396.
Find the 15th multiple of 36.
The 15th multiple of 36 is 15×36 = 540.
Is 725 a multiple of 36?
No, 725 is not a multiple of 36 because it cannot be expressed as 36×n.
FAQs
A multiple of 36 is any number that can be expressed as 36 times an integer. For example, 36, 72, 108, and so on.
A number is a multiple of 36 if it is divisible by both 4 and 9. This is because 36 = 4 × 9.
The first five multiples of 36 are 36, 72, 108, 144, and 180.
Yes, 180 is a multiple of 36 because 36 × 5 = 180.
Multiples of 36 can be useful in scenarios such as calculating area, dividing items into equal groups, and working with data storage sizes.
The prime factorization of 36 is 2² × 3². This means that any multiple of 36 will have at least these prime factors raised to at least these powers.
No, 400 is not a multiple of 36 because it does not meet the divisibility rules for both 4 and 9.
The LCM of 36 and 60 is 180. This is the smallest number that is a multiple of both 36 and 60.
To find the 10th multiple of 36, multiply 36 by 10. So, 36 × 10 = 360.
No, a prime number cannot be a multiple of 36 because a prime number has exactly two distinct positive divisors: 1 and itself, while 36 has more divisors and is not prime.