# Multiples of 3

## What are the Multiples of 3?

In mathematics, multiples of a number are the results of multiplying that number by any integer. In the case of 3, its multiples are obtained by multiplying 3 by any positive or negative whole number. These multiples form a sequence of numbers that are evenly divisible by 3. For example, some multiples of 3 include -6, 0, 3, 6, 9, 12, 15, and so on.

## Ways to find

1. Start with the first multiple of 3, which is 3 itself.
2. Keep adding 3 to the previous multiple to find the next multiple.
3. Repeat step 2 until you reach the desired number of multiples or until you find the desired range.

For example, to find the first five multiples of 3:

• Add 3 to the previous multiple: 3 + 3 = 6 (the second multiple of 3).
• Add 3 to the previous multiple: 6 + 3 = 9 (the third multiple of 3).
• Add 3 to the previous multiple: 9 + 3 = 12 (the fourth multiple of 3).
• Add 3 to the previous multiple: 12 + 3 = 15 (the fifth multiple of 3).

Therefore, the first five multiples are 3, 6, 9, 12, and 15.

You can use a similar approach to find more multiples or to find multiples within a specific range.

## Solved questions

### 1. Find the sum of the first 8 multiples of 3.

The first 8 multiples are 3, 6, 9, 12, 15, 18, 21, 24. Let’s use the formula for the sum in the arithmetic series.

The formula for the sum of an arithmetic series is:
Sum = (n/2) * (first term + last term)

In this case:

The first term is the first multiple of 3, which is 3.
The last term is the eighth multiple of 3, which is 3 * 8 = 24.
The number of terms (n) is 8.

Now, plug the values into the formula:
Sum = (8/2) * (3 + 24)
Sum = 4 * 27
Sum = 108

So, the sum of the first 8 multiples of 3 is 108.

### 2. The sum of the first five multiples of 3 is

The first five multiples are 3, 6, 9, 12, and 15. Let’s use the arithmetic series formula to sum five multiples

The formula for the sum of an arithmetic series is:
Sum = (n/2) * (first term + last term)

• nth term is 5
• the first term is 3
• the last term is 15

Sum = (5/2) * (3 + 15)
= 2.5 * 18 = 45

### 3. The average of the first five multiples of 3 is

To find the average of the first five multiples, you need to sum all the multiples and then divide by the number of multiples (which is 5 in this case).

The first five multiples are 3, 6, 9, 12, 15.

Now, calculate the sum:
Sum = 3 + 6 + 9 + 12 + 15 = 45

Next, calculate the average:
Average = Sum / Number of multiples = 45 / 5 = 9

So, the average of the first five multiples of 3 is 9.

### 4. Find two consecutive multiples of 3 whose product is 648

Let’s find two consecutive multiples of 3 whose product is 648.

1. Start by thinking of multiples: 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on.
2. We want two of these multiples that are right next to each other, like 3 and 6, 6 and 9, 9 and 12, and so on.
3. Now, let’s check the product of each pair. We find that the product of 24 and 27 is 648.

So, the two consecutive multiples of 3 whose product is 648 are 24 and 27.

Do you want an equation to solve this question? Read it

### 5. What is the average of the first 20 multiples of 3

Let’s find the average of the first 20 multiples.

1. First, let’s write down the first 20 multiples: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60
2. Now, let’s add all these numbers together to find the sum: 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 + 33 + 36 + 39 + 42 + 45 + 48 + 51 + 54 + 57 + 60
3. To make it easier, we can group the numbers: (3 + 57) + (6 + 54) + (9 + 51) + (12 + 48) + (15 + 45) + (18 + 42) + (21 + 39) + (24 + 36) + (27 + 33) + (30 + 60)
4. Now, let’s add the grouped numbers: 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 90
5. Add all the numbers together: 600 + 90 = 690
6. Next, find the average by dividing the sum by the number of multiples (which is 20 in this case): Average = Sum / Number of multiples = 690 / 20 = 34.5

So, the average of the first 20 multiples of 3 is 34.5

Read this also: Factors of 64

### 1. What is the first multiple of 3?

The first multiple of 3 is 3.

### 2. What is the next multiple of 3 after 9?

The next multiple of 3 after 9 is 12.

### 3. Can you name three consecutive multiples of 3?

Three consecutive multiples of 3 are 18, 21, and 24.

### 4. What is the sum of the first five multiples of 3?

The sum of the first five multiples of 3 is 45. (3 + 6 + 9 + 12 + 15 = 45)

### 5. Is 27 a multiple of 3?

Yes, 27 is a multiple of 3.

### 6. What is the largest multiple of 3 less than 50?

The largest multiple of 3 less than 50 is 48.

### 7. How many multiples of 3 are there between 10 and 30?

There are 7 multiples of 3 between 10 and 30. (12, 15, 18, 21, 24, 27, 30)

### 8. Find the product of the first four multiples of 3.

The product of the first four multiples of 3 is 162. (3 x 6 x 9 x 12 = 162)

### 9. What is the pattern in the units digit of multiples of 3?

The pattern in the units digit of multiples of 3 is that it repeats in a cycle of 3, 6, 9, 2, 5, 8, 1, 4, 7, 0.

### 10. How would you determine if a number is a multiple of 3?

To determine if a number is a multiple of 3, you can check if the sum of its digits is divisible by 3. If the sum is divisible by 3, then the number is also divisible by 3.