In this chapter of mathematics, you will study about how to find your multiples of 2. You will learn what process you can implement to figure out what is a multiple of 2. In addition, you will study about the special numbers that determine all multiples of 2. You will further learn to identify and distinguish between a factor and a multiple.
For Example: let's take factor of 12
3 Ã— 4 = 12, thus, 3 and 4 are factors of 12
Also, 2 Ã— 6 = 12, thus 2 and 6 are factors of 12 as well,
And 1 Ã— 12 = 12, therefore, 1 and 12 also makes for factors of 12 .
And seeing that, multiplying negatives makes a positive, âˆ’1, âˆ’2, âˆ’3, âˆ’4, âˆ’6 and âˆ’12 are factors of 12 as well:
hence, we have all the factors of 12 that are:
1, 2, 3, 4, 6 and 12 and (âˆ’1), (âˆ’2), (âˆ’3), (âˆ’4), (âˆ’6) and (âˆ’12)
Note: A number or positive integer can have many factors.
Multiples of 3: On a number line, if you see
Multiples of 3: will come out to be 3, 6, 9, 0, âˆ’3, âˆ’6, âˆ’9
15 is a multiple of 3, as in 3 Ã— 5 = 15.
From the description above, we observe that our multiples of 2 are identified simply multiplying any number by 2. We are aware that multiplication means repeated addition. This means that anytime we multiply something by 2, it basically implies that we are adding that number twice.
So, 4 Ã— 2 is 4 + 4 = 8. This also implies that when we see a number being multiplied by 2, we can straight away carry out the addition of that number with itself. Likewise 5 Ã— 2 is 5 + 5 = 10. 7 Ã— 2 = 7 + 7 = 14. So, to make things easier, you can conduct the addition until you have memorized the multiples of 2. Refer to the table below to see what happens as we start to multiply our numbers by 2:
Numbers | Multiplication | Addition | Product |
1 | 1 Ã— 1 | 1 + 1 | 2 |
2 | 2 Ã— 2 | 2 + 2 | 4 |
3 | 3 Ã— 2 | 3 + 3 | 6 |
4 | 4 Ã— 2 | 4 + 4 | 8 |
5 | 5 Ã— 2 | 5 + 5 | 10 |
6 | 6 Ã— 2 | 6 + 6 | 12 |
7 | 7 Ã— 2 | 7 + 7 | 14 |
8 | 8 Ã— 2 | 8 + 8 | 16 |
9 | 9 Ã— 2 | 9 + 9 | 18 |
10 | 10 Ã— 2 | 10 + 10 | 20 |
11 | 11 Ã— 2 | 11 + 11 | 22 |
Do you observe an interesting pattern here? Why, the last digits of multiples of 2 appear to accompany a repeating pattern of 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, etc in a way of spacing of 2 numbers in between each. With this, we can tell that any multiple of 2 will terminate in a 2, 4, 6, 8 or 0. Make a point that if it ends in any other number, then it will not be a multiple of 2. This also makes it certainly simpler to find the multiples of 2.
You need to just begin counting off the pattern and once you get to 8, you need to add 1 to the digits before the last digit. Thus, after 28 comes 30 since 2 + 1 = 3, (the digits before the last digit plus 1), after 78 comes 80 since 7 + 1 = 8.
Q1. What do we Understand by Multiples of 2?
Answer: Multiples of 2 are basically the products of numbers multiplied by 2. Therefore, any number you will multiply by 2 will provide you a multiple of 2.
Q2. What is the Importance of Learning Multiples of 2?
Answer: Now letâ€™s understand why learning about multiples of 2 is important to learn. It is important to learn about multiples of 2 because you will face these numerical based problems often in your math classes and Math examination. Moreover, knowing about the multiples will help you do your calculation better in tests as well in daily life. Being able to identify them, say them, and writing them will enable you to find the answer correctly and quickly.
Q3. How to Identify if a Number M is a Multiple of N?
Answer: For this purpose, we need to divide number M by N. In case the remaining Euclidean division is 0, then M is a multiple of N, and N is a divisor of M. Lets understand this using an example. For Example: Is 30 a multiple of 2? Divide 30 by 2, 30/2 = 15 (integer unaccompanied by the decimals after the decimal point), remain 0, so 30 is a multiple of 2 and 2 is a divisor of 30.
Q4. What are Factors and Multiples?
Answer: Remember that Factors and multiples are two different things. Though they both involve multiplication, the mechanism and purpose is different. That being said,
Factors are what we multiply to obtain the number.
Multiples are what we obtain after multiplying the number by an integer (not a fraction and not in decimal form).
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