Factors and multiples are pertained to each other. A variable of a number is the number the divides it fully without leaving any remainder. For any kind of given number we have the right to represent it together p × q = z. Here we say z is a many of p and also q. According to the an interpretation of factors and also multiples, p and q are determinants of z, due to the fact that z is divisible through p and q. For example, 6 × 2 = 12, so 6 and 2 are the determinants of 12, and 12 is a many of 6 and 2.

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1.How to uncover Factors and also Multiples?
2.Common Factors and also Multiples
3.Properties the Factors and also Multiples
4.FAQs ~ above Factors and Multiples

How to find Factors and also Multiples?


To discover factors and also multiples of any kind of given number, let to speak 'p', we have to find the perform of numbers that divide the number 'p' without leaving any remainder. Right here let united state take an example of number 28. How have the right to we find determinants of 28?

Steps come Find determinants of a Number

Step 1: list the two numbers such the their product provides 28.Step 2: Let's say us take 4 and 7 as the numbers.Step 3: right here 28 is divisible by 4 and 7 there is no leaving any kind of remainder.Step 4: Hence, 28 deserve to be factored in together 28 = 7 × 4.Step 6: factors of 28 can be provided as 1, 2, 4, 7, 14, and also 28.

1 and the number chin are always the components of the particular number.

Finding Multiples the a Number

Multiples of a number room the numbers the we get after multiply the number by a whole number. Here, let us take the same example of number 28. How can we find multiples the 28? The multiples that 28 room all the number that result from the multiplication of 28 by one more whole number. Let us look in ~ the skip counting technique shown in the photo below. The skip counting method is one of the simplest techniques to uncover the multiples of any kind of given number.

Multiples the 28Explanation
2828 × 1
5628 × 2 or 28 + 28
8428 × 3 or 28 + 28 + 28
11228 × 4 or 28 + 28 + 28 + 28
14028 × 5 or 28 + 28 + 28 + 28 + 28
16828 × 6 or 28 + 28 + 28 + 28 + 28 + 28

Here, 28, 56, 84, 112, 140, and 168 room a few multiples that 28. There are limitless multiples of any given number.


Common Factors and Multiples


In this section, you will certainly learn how to find common factors and multiples of any type of number. We know that a element is a number that exactly divides the given number. Hence, a element is nothing yet a divisor that the given number. To find the factors, we have the right to use the multiplication and also the division method. To inspect if 2 or much more numbers have usual factors between them we have the right to follow the listed below steps:

Write the provided numbers.Write every the possible factors that the given numbersFind the factors which are the very same in both the numbers.Encircle the typical factors.

This method we can easily find common factors in between two or much more numbers. Let us look at some examples.

Common determinants of 30 and also 42:

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Therefore, the typical factors of 30 and 42 space 1, 2, 3, and also 6.

Here is an additional example with 3 numbers. The usual factors that 42, 70, and also 84 are shown in the picture below.

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Hence the common factors the 42, 70, and also 84 room 1, 2, 7, and 14. Currently let us look at ways to find common multiples.

There space various techniques to find common multiples. Two of such ways are:

Listing multiples method. In this, we list the multiples of each number and then we find their common multiples. It is just one of the most basic methods by which we can find the typical multiples of two or much more numbers.

Let united state use the Venn chart method. First, mark the multiples of any kind of 2 numbers, let's to speak 3 and also 4 in two different circles. Look for the common numbers coming in both circles. The circle of multiples that 3 intersects with the one of multiples of 4. The intersection component has the usual multiples that belong to 3 and 4. Please note that there are boundless numbers of usual multiples for every pair that numbers. The very first three usual multiples the 3 and also 4 room 12, 24, and also 36.

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Now, let united state look at an instance of the listing multiples method. To find the common multiples that 2 and also 4, us list their multiples and also then find their usual multiples.

Common multiples that 2 and 4: 4, 8, 12, 16, 20, 24, and so on …

If a number is a factor of one more number, then their typical multiples are all the multiples the the larger number (as in the above example).


There are numerous properties of factors and also multiples the will assist you to know this concept properly. Those nature are noted below:

1 is the factor of every number.0 is the many of every number.For every number, 1 is the smallest factor and also that number itself is the largest factor.Every number is a many of itself.There are an infinite variety of multiples and also a finite number of factors possible for every number.

Important Notes

Multiples of any kind of number room infinite. Therefore, a collection of any kind of two numbers can have one infinite number of common multiples.

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Example 2: What room the factors and multiples the 60?

Solution:

The determinants of 60 room all the whole numbers that deserve to divide 60 there is no leaving any type of remainder. So, the components of 60 space 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. The mutiples that 60 can be discovered by multiplying 60 with entirety numbers starting from 1.60 × 1 = 6060 × 2 = 12060 × 3 = 18060 × 4 = 24060 × 5 = 300So, the perform of multiples of 60 consists of 60, 120, 180, 240, 300, and also so on.Therefore, the factors and also multiples the 60 are:Factors = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and also 60Multiples = 60, 120, 180, 240, 300, ...


Example 3: discover the typical factors and also multiples that 4, 8, and also 12.

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Solution: To find the typical factors and also multiples of 4, 8, and 12 us will usage the listing method.Let united state write separately components of 4,8 and 12. There are 3 components of 4 which room 1, 2, and also 4. There room 4 components of 8 provided as 1, 2, 4, and also 8. There space 6 determinants of 12 which space 1, 2, 3, 4, 6, and also 12.The typical factors of 4, 8, and 12 room 1, 2, and also 4.Let us make a perform of multiples that 4, 8, and 12.Multiples that 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72 ...Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 ...Multiples that 12 = 12, 24, 36, 48, 60, 72, ...So, the typical multiples of 4, 8, and also 12 room 24, 48, 72, ...