Multiples Of Numbers: Find Sets And Two-Digit Multiples

Nov 9, 2025 by Admin 56 views

Hey guys! Today, we're diving into the fascinating world of multiples. We'll be tackling how to find the first few multiples of a number and then figuring out which two-digit numbers are multiples of specific numbers. So, grab your thinking caps, and let's get started!

Determining the First 5 Multiples of a Number

Let's break down how to determine the set formed by the first 5 multiples of a number. This concept is fundamental in number theory and helps in understanding divisibility rules and patterns. To find the first five multiples of a given number, you simply multiply that number by the first five positive integers (1, 2, 3, 4, and 5). Let's walk through each example to make sure we understand it perfectly.

a) Multiples of 5

To find the first five multiples of 5, we multiply 5 by 1, 2, 3, 4, and 5. So, we have:

5 * 1 = 5
5 * 2 = 10
5 * 3 = 15
5 * 4 = 20
5 * 5 = 25

Therefore, the set of the first five multiples of 5 is {5, 10, 15, 20, 25}. See, it's pretty straightforward when you break it down! Each number in this set is perfectly divisible by 5, leaving no remainder. This is the essence of what a multiple is.

b) Multiples of 7

Next up, let's find the first five multiples of 7. We'll use the same process as before, multiplying 7 by 1, 2, 3, 4, and 5:

7 * 1 = 7
7 * 2 = 14
7 * 3 = 21
7 * 4 = 28
7 * 5 = 35

So, the set of the first five multiples of 7 is {7, 14, 21, 28, 35}. Notice how each of these numbers can be divided by 7 without any remainder? That's the magic of multiples!

c) Multiples of 10

Now, let's tackle the first five multiples of 10. This one is particularly easy because multiplying by 10 simply adds a zero to the end of the number. Let's see:

10 * 1 = 10
10 * 2 = 20
10 * 3 = 30
10 * 4 = 40
10 * 5 = 50

Thus, the set of the first five multiples of 10 is {10, 20, 30, 40, 50}. You'll notice that all multiples of 10 end in zero, which is a handy trick to remember.

d) Multiples of 15

Let's move on to finding the first five multiples of 15. We follow the same multiplication pattern:

15 * 1 = 15
15 * 2 = 30
15 * 3 = 45
15 * 4 = 60
15 * 5 = 75

Therefore, the set of the first five multiples of 15 is {15, 30, 45, 60, 75}. These numbers are all divisible by 15, and you can see how they increase by 15 each time.

e) Multiples of 20

Finally, let's determine the first five multiples of 20. Again, we multiply 20 by the first five positive integers:

20 * 1 = 20
20 * 2 = 40
20 * 3 = 60
20 * 4 = 80
20 * 5 = 100

So, the set of the first five multiples of 20 is {20, 40, 60, 80, 100}. Just like multiples of 10, multiples of 20 have a pattern – they often end in zero, making them easier to spot.

Understanding how to find multiples is essential for more advanced math topics. It's like building a strong foundation for a house; you need the basics down before you can build something complex! So, now that we've nailed this, let's move on to the next challenge: finding two-digit multiples.

Writing the Set of Two-Digit Multiples

Now, let's shift gears and focus on writing the set of two-digit numbers that are multiples of specific numbers. This task combines our understanding of multiples with the practical skill of identifying numbers within a certain range (in this case, two-digit numbers, which range from 10 to 99). It's like a mathematical scavenger hunt, where we're looking for numbers that fit our criteria. This is a crucial skill because it enhances our ability to recognize patterns and apply divisibility rules in various contexts.

a) Two-Digit Multiples of 8

To find the two-digit multiples of 8, we need to identify all numbers between 10 and 99 that are divisible by 8. The easiest way to do this is to start with the smallest multiple of 8 that is greater than or equal to 10 and then keep adding 8 until we reach a number greater than 99. Let's start by dividing 10 by 8. The result is 1 with a remainder, so we need to go to the next whole number, which is 2. Thus, 8 multiplied by 2 is our starting point:

8 * 2 = 16

Now, we just keep adding 8 to find the next multiples:

16 + 8 = 24
24 + 8 = 32
32 + 8 = 40
40 + 8 = 48
48 + 8 = 56
56 + 8 = 64
64 + 8 = 72
72 + 8 = 80
80 + 8 = 88
88 + 8 = 96

If we add 8 again, we get 104, which is a three-digit number, so we stop here. Therefore, the set of two-digit multiples of 8 is {16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}. It's a bit like climbing a staircase, where each step is 8 units higher!

b) Two-Digit Multiples of 10

Finding two-digit multiples of 10 is much simpler. We know that multiples of 10 end in zero, so we just need to list the two-digit numbers that end in zero. These are:

10, 20, 30, 40, 50, 60, 70, 80, 90

Thus, the set of two-digit multiples of 10 is {10, 20, 30, 40, 50, 60, 70, 80, 90}. Multiples of 10 are super useful in everyday math, like when we're counting money or measuring things.

c) Two-Digit Multiples of 11

Let's find the two-digit multiples of 11. The multiples of 11 have a neat pattern: they're the numbers where both digits are the same. So, we just need to list those numbers between 10 and 99:

11, 22, 33, 44, 55, 66, 77, 88, 99

Therefore, the set of two-digit multiples of 11 is {11, 22, 33, 44, 55, 66, 77, 88, 99}. This pattern is one of those cool math shortcuts that make you feel like a pro!

d) Two-Digit Multiples of 15

Finally, let's tackle the two-digit multiples of 15. We need to find numbers between 10 and 99 that are divisible by 15. We can start by multiplying 15 by small integers until we get a two-digit number:

15 * 1 = 15
15 * 2 = 30
15 * 3 = 45
15 * 4 = 60
15 * 5 = 75
15 * 6 = 90

If we multiply 15 by 7, we get 105, which is a three-digit number, so we stop here. Thus, the set of two-digit multiples of 15 is {15, 30, 45, 60, 75, 90}. Identifying multiples like this helps us with division and understanding number relationships.

Conclusion

So, there you have it, guys! We've explored how to find the first five multiples of a number and how to identify two-digit multiples. These are fundamental skills in mathematics, and mastering them will set you up for success in more advanced topics. Remember, math isn't just about numbers; it's about patterns and problem-solving. Keep practicing, and you'll become a math whiz in no time! Whether it's recognizing the pattern in multiples of 11 or listing out multiples of 8, you're building a solid foundation for your mathematical journey. Keep up the great work!