Multiples

# What are the Multiples of 31 | All Multiples of 31 up to 1000

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What are the Multiples of 31 | All Multiples of 31 up to 1000

**The first ten multiples of 31 are 31, 62, 93, 124, 155, 186, 217, 248, 279, and 310.**

The multiples of 31 are a sequence of numbers that can be obtained by multiplying the number 31 with a sequence of natural numbers.

The difference between any two consecutive numbers in the sequence of multiples of 31 is always 31.

To find the multiples of 31, you need to perform a repeated addition of the number 31 or multiply the number 31 with a sequence of natural numbers.

The list of the natural numbers which can be completely divided by the number 31 and leave a remainder of zero are the multiples of 31. In this article, we will discuss the multiples of 31 and how to calculate them in a simple way.

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**What are the first five Multiples of 31?**

To find the first five multiples of 31, we will have to multiply the numbers 31 by 1, 2, 3, 4, and 5. The detailed steps are given below:

Step 1: To find the first multiple of 31, multiply 31 by 1. 31 X 1 = 31.

Step 2: To find the second multiple of 31, multiply 31 by 2. 31 X 2 = 62. Alternatively, you can add 31 to the first multiple to get the second multiple of 31. 31 + 31 = 62.

Step 3: Multiply 31 by 3 to get the third multiple of 31. 31 X 3 = 93. Also, you can add 31 two times to the second multiple to get the third multiple of 31. 62 + 31 = 93.

Step 4: The fourth multiple of 31 can be found by multiplying 31 by 4. 31 X 4 = 124. Adding 31 three times will also give the fourth multiple of 31. 31 + 31 + 31 + 31 = 124.

Step 5: To find the fifth multiple of 31, you need to multiply 31 by 5. 31 x 5 = 155. Adding 31 four times will give us the fifth multiple of 31. 31 + 31 + 31 + 31 + 31 = 155.

Hence the first 5 multiples of 31 are 31, 62, 93, 124, and 155.

**How to find the Multiples of 31?**

We can find the multiples of 31 in two different ways. The two different ways are listed below: the first is using the way of repeated addition and the other way is by multiplication method.

**Finding multiples of 31 using the repeated addition method**

Using the repeated addition method, 31 itself will be the first multiple of 31. To obtain the second multiple of 31, add the sum of the first multiple with 31, i.e., 31+31=62. An example of the first five multiples of 31 using the repeated addition method is given below:

31

31+31=62

62+31=93

93+31=124

124+31=155

**Finding multiples of 31 using the multiplication method**

31 X 1 | 31 |

31 X 2 | 62 |

31 X 3 | 93 |

31 X 4 | 124 |

31 X 5 | 155 |

31 X 6 | 186 |

**Finding the first 20 Multiples of 31**

To find the first 20 multiples of 31 using the multiplication method, you can create a table with the sequence of numbers from 1 to 20 and multiply 31 with each number in the sequence. The first 20 multiples of 31 are given below:

31 X 1 | 31 |

31 X 2 | 62 |

31 X 3 | 93 |

31 X 4 | 124 |

31 X 5 | 155 |

31 X 6 | 186 |

31 X 7 | 217 |

31 X 8 | 248 |

31 X 9 | 279 |

31 X 10 | 310 |

31 X 11 | 341 |

31 X 12 | 372 |

31 X 13 | 403 |

31 X 14 | 434 |

31 X 15 | 465 |

31 X 16 | 496 |

31 X 17 | 527 |

31 X 18 | 558 |

31 X 19 | 589 |

31 X 20 | 620 |

**What are the multiples of 31 up to 1000**

31 | 62 | 93 | 124 | 155 | 186 | 217 | 248 |

279 | 310 | 341 | 372 | 403 | 434 | 465 | 527 |

558 | 589 | 620 | 651 | 682 | 713 | 744 | 775 |

806 | 837 | 868 | 899 | 930 | 961 | 992 | – |

**Difference between Multiples and Factors of 31**

Multiples and factors are related concepts in mathematics, but they have different meanings.

Factors | Multiples |

Factors of 31, on the other hand, are numbers that divide evenly into 31. In other words, they are integers that, when multiplied by another integer, result in 31. The factors of 31 are 1 and 31 because no other integer divides into 31 without leaving a remainder. | Multiples of 31 are numbers that are obtained by multiplying 31 by another integer. For example, the first few multiples of 31 are 31, 62, 93, 124, and so on. Multiples of 31 form a sequence that goes on indefinitely, with each term being 31 more than the previous one. |

In summary, multiples of 31 are obtained by multiplying 31 by other integers, while factors of 31 are the integers that divide into 31 without leaving a remainder.

**Solved Examples for Multiples of 31**

**What is the 10th multiple of 31?**

To find the 10th multiple of 31, we can multiply 31 by 10:

10 x 31 = 310

So the 10th multiple of 31 is 310.

**Is 217 a multiple of 31?**

To determine whether 217 is a multiple of 31, we need to check if there is an integer k such that:

k x 31 = 217

We can see that there is no such integer k that would satisfy this equation, so 217 is not a multiple of 31.

**Find the next three multiples of 31 after 155.**

To find the next three multiples of 31 after 155, we can add 31 to 155 three times:

155 + 31 = 186

186 + 31 = 217

217 + 31 = 248

So the next three multiples of 31 after 155 are 186, 217, and 248.

**Write the first five multiples of 31 in descending order.**

The first five multiples of 31 are:

31, 62, 93, 124, 155

To write them in descending order, we simply list them in reverse order:

155, 124, 93, 62, 31

**Find the sum of the first 12 multiples of 31.**

To find the sum of the first 12 multiples of 31, we can use the formula for the sum of an arithmetic series:

Sn = n/2 x (a1 + an)

where Sn can be termed as the sum of the first n terms, a1 should be the first term, and an should be the nth term.

In this case, n = 12, a1 = 31, and an = 372 (the 12th multiple of 31).

Putting the values into the formula, we get:

Sn = 12/2 x (31 + 372)

Sn = 6 x 403

Sn = 2418

So the sum of the first 12 multiples of 31 is 2418.

**What is the smallest multiple of 31 that is also a multiple of 13?**

To find the smallest multiple of 31 that is also a multiple of 13, we need to find the least common multiple (LCM) of 31 and 13. We can do this by listing the multiples of each number until we find the first common multiple:

Multiples of 13: 13, 26, 39

Multiples of 31: 31, 62

The first common multiple is 62, which is the second multiple of 31. Therefore, the smallest multiple of 31 which is also a multiple of 13 is 62.

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**FAQs on Multiples of 31**

### What are the first five multiples of 31?

The first five multiples of 31 are 31, 62, 93, 124, and 155.

### Is 62 a multiple of 31?

Yes, 62 is a multiple of 31 because 62 divided by 31 equals 2 with no remainder.

### How do you determine if a number is a multiple of 31?

To determine if a number is a multiple of 31, you need to check if there is an integer k such that k multiplied by 31 equals the given number. If there is such an integer, then the number is a multiple of 31. Otherwise, it is not a multiple of 31.

### What is the 20th multiple of 31?

To find the 20th multiple of 31, you can multiply 31 by 20. Therefore, the 20th multiple of 31 is 620.

### How do you find the sum of the first n multiples of 31?

To find the sum of the first n multiples of 31, you can use the formula for the sum of an arithmetic series: Sn = n/2 x (a1 + an), where Sn can be termed as the sum of the first n terms, a1 should be the first term, and an should be the nth term. You can substitute the values of n, a1, and add to find the sum.

### What is the smallest multiple of 31 that is also a multiple of 7?

To find the smallest multiple of 31 which is also a multiple of 7, we need to find the least common multiple (LCM) of 31 and 7. We can do this by listing the multiples of each number until we find the first common multiple:

Multiples of 7: 7, 14, 21, 28, 35

Multiples of 31: 31, 62

The first common multiple is 217, which is 7 times 31. Therefore, the smallest multiple of 31 which is also a multiple of 7 is 217.

Written by

Prerit Jain