Multiples of 31

Multiples of 31 are integers obtained by multiplying 31 with other whole numbers. In mathematics, a multiple of 31 can be represented as $\mathrm{31n}$, where $n$ is an integer. This process involves multiplication, producing numbers like 31, 62, 93, and so on. Factors and divisors of these multiples include both 31 and the integer used in the multiplication. Understanding multiples of 31 helps in various mathematical problems involving divisibility and common factors.

What are Multiples of 31?

Multiples of 31 are the products obtained by multiplying 31 by any integer. Examples include 31, 62, 93, 124, and so on. These numbers follow the pattern 31n, where n is any integer.

Prime Factorization of 31: 31¹ First 10 Multiples of 31 are 31, 62, 93, 124, 155, 186, 217, 248, 279, 310.

For example, 93, 155, 217 and 279 are all multiples of 31, 320 is not a multiple of 31 for the following reasons:

Number	Calculation	Reason	Remainder
93	93÷31 = 3	93 is a multiple of 31 because it divides evenly.	0
155	155÷31 = 5	155 is a multiple of 31 because it divides evenly.	0
217	217÷31 = 7	217 is a multiple of 31 because it divides evenly.	0
279	279÷31 = 9	279 is a multiple of 31 because it divides evenly.	0
320	320÷31 = 10	320 is not a multiple of 31 because it does not divide evenly.	10

List of First 100 Multiples of 31 with Remainders

Number	Reason	Remainder
31	31 is a multiple of 31 because 31 × 1 = 31	0
62	62 is a multiple of 31 because 31 × 2 = 62	0
93	93 is a multiple of 31 because 31 × 3 = 93	0
124	124 is a multiple of 31 because 31 × 4 = 124	0
155	155 is a multiple of 31 because 31 × 5 = 155	0
186	186 is a multiple of 31 because 31 × 6 = 186	0
217	217 is a multiple of 31 because 31 × 7 = 217	0
248	248 is a multiple of 31 because 31 × 8 = 248	0
279	279 is a multiple of 31 because 31 × 9 = 279	0
310	310 is a multiple of 31 because 31 × 10 = 310	0
341	341 is a multiple of 31 because 31 × 11 = 341	0
372	372 is a multiple of 31 because 31 × 12 = 372	0
403	403 is a multiple of 31 because 31 × 13 = 403	0
434	434 is a multiple of 31 because 31 × 14 = 434	0
465	465 is a multiple of 31 because 31 × 15 = 465	0
496	496 is a multiple of 31 because 31 × 16 = 496	0
527	527 is a multiple of 31 because 31 × 17 = 527	0
558	558 is a multiple of 31 because 31 × 18 = 558	0
589	589 is a multiple of 31 because 31 × 19 = 589	0
620	620 is a multiple of 31 because 31 × 20 = 620	0
651	651 is a multiple of 31 because 31 × 21 = 651	0
682	682 is a multiple of 31 because 31 × 22 = 682	0
713	713 is a multiple of 31 because 31 × 23 = 713	0
744	744 is a multiple of 31 because 31 × 24 = 744	0
775	775 is a multiple of 31 because 31 × 25 = 775	0
806	806 is a multiple of 31 because 31 × 26 = 806	0
837	837 is a multiple of 31 because 31 × 27 = 837	0
868	868 is a multiple of 31 because 31 × 28 = 868	0
899	899 is a multiple of 31 because 31 × 29 = 899	0
930	930 is a multiple of 31 because 31 × 30 = 930	0
961	961 is a multiple of 31 because 31 × 31 = 961	0
992	992 is a multiple of 31 because 31 × 32 = 992	0
1023	1023 is a multiple of 31 because 31 × 33 = 1023	0
1054	1054 is a multiple of 31 because 31 × 34 = 1054	0
1085	1085 is a multiple of 31 because 31 × 35 = 1085	0
1116	1116 is a multiple of 31 because 31 × 36 = 1116	0
1147	1147 is a multiple of 31 because 31 × 37 = 1147	0
1178	1178 is a multiple of 31 because 31 × 38 = 1178	0
1209	1209 is a multiple of 31 because 31 × 39 = 1209	0
1240	1240 is a multiple of 31 because 31 × 40 = 1240	0
1271	1271 is a multiple of 31 because 31 × 41 = 1271	0
1302	1302 is a multiple of 31 because 31 × 42 = 1302	0
1333	1333 is a multiple of 31 because 31 × 43 = 1333	0
1364	1364 is a multiple of 31 because 31 × 44 = 1364	0
1395	1395 is a multiple of 31 because 31 × 45 = 1395	0
1426	1426 is a multiple of 31 because 31 × 46 = 1426	0
1457	1457 is a multiple of 31 because 31 × 47 = 1457	0
1488	1488 is a multiple of 31 because 31 × 48 = 1488	0
1519	1519 is a multiple of 31 because 31 × 49 = 1519	0
1550	1550 is a multiple of 31 because 31 × 50 = 1550	0
1581	1581 is a multiple of 31 because 31 × 51 = 1581	0
1612	1612 is a multiple of 31 because 31 × 52 = 1612	0
1643	1643 is a multiple of 31 because 31 × 53 = 1643	0
1674	1674 is a multiple of 31 because 31 × 54 = 1674	0
1705	1705 is a multiple of 31 because 31 × 55 = 1705	0
1736	1736 is a multiple of 31 because 31 × 56 = 1736	0
1767	1767 is a multiple of 31 because 31 × 57 = 1767	0
1798	1798 is a multiple of 31 because 31 × 58 = 1798	0
1829	1829 is a multiple of 31 because 31 × 59 = 1829	0
1860	1860 is a multiple of 31 because 31 × 60 = 1860	0
1891	1891 is a multiple of 31 because 31 × 61 = 1891	0
1922	1922 is a multiple of 31 because 31 × 62 = 1922	0
1953	1953 is a multiple of 31 because 31 × 63 = 1953	0
1984	1984 is a multiple of 31 because 31 × 64 = 1984	0
2015	2015 is a multiple of 31 because 31 × 65 = 2015	0
2046	2046 is a multiple of 31 because 31 × 66 = 2046	0
2077	2077 is a multiple of 31 because 31 × 67 = 2077	0
2108	2108 is a multiple of 31 because 31 × 68 = 2108	0
2139	2139 is a multiple of 31 because 31 × 69 = 2139	0
2170	2170 is a multiple of 31 because 31 × 70 = 2170	0
2201	2201 is a multiple of 31 because 31 × 71 = 2201	0
2232	2232 is a multiple of 31 because 31 × 72 = 2232	0
2263	2263 is a multiple of 31 because 31 × 73 = 2263	0
2294	2294 is a multiple of 31 because 31 × 74 = 2294	0
2325	2325 is a multiple of 31 because 31 × 75 = 2325	0
2356	2356 is a multiple of 31 because 31 × 76 = 2356	0
2387	2387 is a multiple of 31 because 31 × 77 = 2387	0
2418	2418 is a multiple of 31 because 31 × 78 = 2418	0
2449	2449 is a multiple of 31 because 31 × 79 = 2449	0
2480	2480 is a multiple of 31 because 31 × 80 = 2480	0
2511	2511 is a multiple of 31 because 31 × 81 = 2511	0
2542	2542 is a multiple of 31 because 31 × 82 = 2542	0
2573	2573 is a multiple of 31 because 31 × 83 = 2573	0
2604	2604 is a multiple of 31 because 31 × 84 = 2604	0
2635	2635 is a multiple of 31 because 31 × 85 = 2635	0
2666	2666 is a multiple of 31 because 31 × 86 = 2666	0
2697	2697 is a multiple of 31 because 31 × 87 = 2697	0
2728	2728 is a multiple of 31 because 31 × 88 = 2728	0
2759	2759 is a multiple of 31 because 31 × 89 = 2759	0
2790	2790 is a multiple of 31 because 31 × 90 = 2790	0
2821	2821 is a multiple of 31 because 31 × 91 = 2821	0
2852	2852 is a multiple of 31 because 31 × 92 = 2852	0
2883	2883 is a multiple of 31 because 31 × 93 = 2883	0
2914	2914 is a multiple of 31 because 31 × 94 = 2914	0
2945	2945 is a multiple of 31 because 31 × 95 = 2945	0
2976	2976 is a multiple of 31 because 31 × 96 = 2976	0
3007	3007 is a multiple of 31 because 31 × 97 = 3007	0
3038	3038 is a multiple of 31 because 31 × 98 = 3038	0
3069	3069 is a multiple of 31 because 31 × 99 = 3069	0
3100	3100 is a multiple of 31 because 31 × 100 = 3100	0

Read More About Multiples of 31

Table of 31

Important Notes

Definition:

• Multiples of 31 are numbers that can be expressed as 31 times an integer. Mathematically, a multiple of 31 is in the form 31×n, where n is an integer.

Sequence:

• The sequence of multiples of 31 starts at 31 and increases by 31 with each subsequent multiple: 31, 62, 93, 124, 155, 186, etc.

Divisibility Rule:

• A number is a multiple of 31 if, after dividing it by 31, the result is an integer without any remainder. For example, 155 is a multiple of 31 because 155÷31 = 5, which is an integer.

Properties:

Multiples of 31 share certain properties:

• They are evenly spaced on the number line, with a constant difference of 31 between consecutive multiples.
• Every multiple of 31 is also a multiple of 1, 31, and their divisors (if any).

Applications:

• Multiples of 31 can be useful in various mathematical and practical contexts, such as finding common multiples in problem-solving, understanding patterns in number theory, and solving equations that involve factors of 31.

Examples on Multiples of 31

Simple Multiples

• 31×1 = 31
• 31×2 = 62
• 31×3 = 93

Larger Multiples

• 1×20 = 620
• 1×50 = 1550
• 31×100 = 310

Real-Life Examples

• Days in a month: Most months have 30 or 31 days. For example, January has 31 days which is a multiple of 31 (31×1).
• Calendar years: 1860 is a multiple of 31 (31×60 = 1860).

Practical Examples of Multiples of 31

What is the 15th multiple of 31?

The 15th multiple of 31 is 31×15 = 465.

Is 248 a multiple of 31?

No, 248 is not a multiple of 31 because it cannot be expressed as 31×n.

What is the next multiple of 31 after 62?

The next multiple of 31 after 62 is 62+31 = 93.

Find the 25th multiple of 31.

The 25th multiple of 31 is 31×25 = 775.

Is 961 a multiple of 31?

Yes, 961 is a multiple of 31 because 31×31 = 961.

FAQs