How many 3-digit numbers are multiples of 7?
3-digit Multiples Counter
Now you know how many 3-digit numbers are multiples of 7. Here you can get all the 3-digit numbers that are multiples of a different number.How many 3-digit numbers are multiples of 8?
Here is the next number of 3-digit numbers of multiples we have counted for you. Copyright | Privacy Policy | Disclaimer | ContactThe first ten multiples of 3 are listed below: $$ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. $$
The multiples of 6 in the list are highlighted in larger, bold face: $$ 3, {\bf{\large 6}}, 9, {\bf{\large 12}}, 15, {\bf{\large 18}}, 21, {\bf{\large 24}}, 27, {\bf{\large 30}}. $$ It appears as if every other number in the sequence is a multiple of 6. In order to see why, here is a picture showing 10 $\times$ 3:
Notice that 2 groups of three make 1 group of six. This can be seen in the picture as 1 group of three purple squares and 1 group of three white squares.
So with an even number of threes, we can group them in pairs to make sixes. When there is an odd number of threes, there are some groups of six with a leftover group of three: in the picture, an odd number of threes leaves a purple group which does not match up with a white group (or vice versa).
The only number in the list that is a multiple of 7 is 21 which is $7 \times 3$. If we write the list of multiples of 7: $$\begin{align} 7, 14, {\bf{\large 21}},& \\ 28, 35, {\bf{\large 42}},& \\ 49, 56, {\bf{\large 63}},& \\ 70, 77, {\bf{\large 84}}& \\ \end{align}$$ and then extend the list of multiples of 3: $$\begin{align} 3, 6, 9, 12, 15, 18, {\bf{\large 21}}, & \\ 24, 27, 30, 33, 36, 39, {\bf{\large 42}}, & \\ 45, 48, 51, 54, 57, 60, {\bf{\large 63}}, & \\ 66, 69, 72, 75, 78, 81, {\bf{\large 84}} \end{align}$$ we can see that the first four multiples of 7 that appear in the list of multiples of 3 are 21, 42, 63, and 84.
21 is $3\times7$.
We got 42 as a multiple of 7 because $42=6\times 7$. We can rewrite it as follows: $$6\times7 = (2\times3)\times7 = 2\times(3\times7) = 2\times 21$$ This is the same as 2 groups of 21. The next one they have in common is 63, which came from $9\times7$. As before, we can see that this is a multiple of 21: $$9\times7 = (3\times3)\times7 = 3\times(3\times7) = 3\times 21$$ In general, the multiples of 7 that appear in the list of multiples of 3 are also multiples of 21, and these happen each 7th multiple of 3 because each seven groups of 3 make a multiple of 7.
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A multiple of 7 is a number that can be divided by 7 leaves the remainder zero and Multiples of 7 are the product of 7 and natural numbers. 7 is a unique number in math, However, in this lesson, you will be introduced how to calculate the multiples of 7 using skip counting method. Lets learn more about multiples of 7 in the tabular form with examples.
- First five multiples of 7: 7, 14, 21, 28, 35.
- Prime Factorization of 7: 1 × 7
Let us recall a little about multiplication tables. Multiples of 7 are the numbers obtained by multiplying 7 with other numbers. The first five multiples of 7 are 7, 14, 21, 28, and 35.
First 20 multiples of 7 are derived by multiplying 7 with 1-20 natural numbers. The obtained resultant is the multiple of 7. Let us look at the list the first 20 multiples of 7:
| 7 × 1 | 7 |
| 7 × 2 | 14 |
| 7 × 3 | 21 |
| 7 × 4 | 28 |
| 7 × 5 | 35 |
| 7 × 6 | 42 |
| 7 × 7 | 49 |
| 7 × 8 | 56 |
| 7 × 9 | 63 |
| 7 × 10 | 70 |
| 7 × 11 | 77 |
| 7 × 12 | 84 |
| 7 × 13 | 91 |
| 7 × 14 | 98 |
| 7 × 15 | 105 |
| 7 × 16 | 112 |
| 7 × 17 | 119 |
| 7 × 18 | 126 |
| 7 × 19 | 133 |
| 7 × 20 | 140 |
To understand the concept of finding multiples, let us take a few more examples.
- Multiples of 20 - The first five multiples of 20 are 20, 40, 60, 80, 100
- Multiples of 4 - The first five multiples of 4 are 4, 8, 12, 16, 20
- Multiples of 5 - The first five multiples of 5 are 5, 10, 15, 20, 25
- Multiples of 3 - The first five multiples of 3 are 3, 6, 9, 12, 15
- Multiples of 6 - The first five multiples of 6 are 6, 12, 18, 24, 30
- Every number is the smallest multiple of itself.
- Number 7 has infinite multiples as it can be multiplied with any whole number and we have infinite whole numbers.
- A multiple can be the common multiple of two or more numbers. Example: 20 is the common multiple of 2, 4, 5, 10,and 20.
- All the multiples of 7are alternatively odd and even numbers.
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Example 1 Sebastian has 2 baskets of apples. Basket 1 contains 16 apples and basket 2 contains 35 apples. Can he sort the apples in each basket into groups of 7 using multiples of 7?
Solution
If 7 divides the number of apples exactly, they can be sorted into groups of 7 14 ÷ 7 leaves a remainder 2 and cannot be sorted into groups of 7 But 35 ÷ 7 = 5 and leaves a remainder 0 so it can be grouped into 5 groups of 7
Apples in basket 1 cannot be sorted into groups of 7 while those in basket 2 can be.
Example 2 Audrey has to determine how many weeks are there in a year?
Solution
Audrey knows there are 365 days in a year. One week has 7 days. To determine how many weeks are there in a year, Audrey will use the following steps: 365 ÷ 7, quotient =52 and remainder = 1. There are approximately 52 weeks in a year.
Audrey determined that there are 52 weeks in a year.
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The first 5 multiples of 7 are 7, 14, 21, 28, and 35.
2. What are common multiples of 7 and 11?
The products which we see in multiplication tables of both 7 and 11 are the common multiples of 7 and 11 For example 77, 154, 231, 308, 385, and so on.
3. What is the least common multiple of 7 and 10?
The least common multiple of 7 and 10 is 70.
4. How do you find multiples of 7?
By multiplying 7 to natural numbers we can get its multiples of 7.
5. What is a multiple of 7 and a factor of 7?
7 is the multiple of 7 and also a factor of 7.