Factors and Multiples

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In the starting level, the factors and the multiples are two of the key concepts that are studied together. Factors are the numbers that divide the given number exactly, whereas multiples are the numbers that are multiplied by the opposite number to urge specific numbers. It is the time to recollect and understand the concept of the multiples and factors of a number. In this article, we are going to know what is a factor of a number and what is a multiple of a number.


What is a Factor of a Number?

Let’s discuss what is a factor of a number. When a number is claimed to be an element of the other second number, then the primary number must divide the second number completely without leaving any remainder. In simple words, if variety (dividend) is strictly divisible by any number (divisor), then the divisor may be a factor of that dividend. Every number features a common divisor that's one and therefore the number itself.

For example, 4 may be a factor of 24, i.e. four divides 24 exactly by giving 6 as the quotient and leaving zero as the remainder. Alternatively, 6 is additionally an element of 24 because it gives 4 as quotient on division. Therefore, 24 has 1, 24, 4, 6 as its factors additionally to 2, 3, 8, and 12 and everyone these numbers divide 24 exactly leaving no remainder.

If any number has only two factors, i.e. 1 and the number itself as its factors, such numbers are known as prime numbers. 2 is an example for a prime number because it has only two factors, which is 1 and 2. Now we know what is a factor of a number, let’s discuss what are multiples.


What are Multiples?

Let’s know what are multiples. A multiple of variety may be a number that's the merchandise of a given number and a few other numbers . Multiples can be observed in a multiplication table. Multiples of some numbers are as follows:

Multiples of 2 are known to be 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and so on Therefore, multiples of 2 will be even numbers and will end with 0, 2, 4, 6 or 8.

Multiples of three are 3, 6, 9, 12, 15, 18, 21, and so on.

Multiples of 5 are known to be  5, 10, 15, 20, 25, and so on.

Every multiple for 5 has its last digit to be 0 or 5.

In the above-mentioned examples, say multiples of two , the amount 2 is often multiplied by infinite numbers to seek out the “n” number of multiples. Now, let us assume an example:

3 × 4 = 12

Given here, 3 and 4 are the two factors of 12,

12 is multiple of 3 and 4

Therefore, we can put up a conclusion that if X and Y are two numbers and;

  • If X divides Y, X may be a factor of Y

  • If Y divides X, then Y is known to be a multiple of X

Since the amount 1 divides every integer, it's a standard factor of each integer. And, every of the numbers is divisible by 1 and every number is a multiple of 1.

Now we know what is a multiple in Math.


Difference Between Factors and Multiples

The difference between the factors and the multiples are given here in a tabular form. Check the table below to understand the difference between them.

S.No

Factors

Multiples

1

The factors are defined as the exact divisors for the given number

The multiples are defined as the numbers which are obtained when multiplied by the other numbers

2

The number of factors is finite

The number of multiplies is infinite

3

The operation helps to find that the factors is a division

The operation helps to find that the multiples is a multiplication

4

Output for the factors should be ≤ to the given number

The outcome of the multiples should be ≥ to the given number


Factors and Multiples Examples

Example 1: 

Find the factors of 20.

Solution:

The factors for 20 are known to be 1, 2, 4, 5, 10 and 20.

Reason is the number 20 is exactly divisible by these given numbers leaving the remainder to be zero.

Example 2: 

Find the multiples of 20.

Solution:

The multiples for 20 are known to be 20, 40, 60, 80, 100, 120, …

Because

20 × 1 = 20,

20 ×2 = 40,

20 ×3 = 60

20 ×4 = 80

20 ×5 = 100, and so on

FAQ (Frequently Asked Questions)

Question 1) Is 6 a Multiple or a Factor?

Answer) 2* 3 = 6 , 36 = 6*6 is both a factor and a multiple.

Question 2) What are Multiples in maths?

Answer) Multiples are really just extended times tables. The multiples of two are all the numbers within the 2 times table, such as 2, 4, 6, 8, 10, and so on. Multiples of 2 always end with a 2, 4, 6, 8, or 0. You can tell 2286, for instance, may be a multiple of two because it ends with a 6.

Question 3) What is a Multiple of a number?

Answer) In science, a multiple is the product for any of the quantity and an integer. In other words, for the quantities a and b, we are saying that b may be a multiple of a if b = na for a few integers n, which is named the multiplier.

Question 4) What are Multiples of 20?

Answer) 20 ,40  ,60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340,360, 380, 400, 420.

Question 5) What are Factors and Multiples?

Answer) Factors and multiples are two different things. But they both are involved in multiplication:

  • Factors are what we will multiply to urge the amount

  • Multiples are what we get after multiplying the amount by an integer (not a fraction).