Factors and Multiples by using Division Facts

Factors and multiples by using division facts are explained here. With the help of this operation we shall learn some other terms.

Consider the following factors and multiples by using division facts:

(i)

$Factors and Multiples by using Division Facts$

15 is not completely divisible by 2

i.e., 14 ÷ 2 = 7 or dividend ÷ divisor = quotient

When a number (dividend) is completely divided by another number (divisor), then this divisor is called a factor and the dividend is called a multiple of the divisor.

Here 2 is the factor of the multiple 14.

14 ÷ 1 = 14, 14 ÷ 14 = 1, 14÷ 7 = 2

So the divisors 1, 14 and 7 are also the complete divisors or factors of the dividend (multiple) 14.

Thus, the factor must be a complete divisor of the multiple (dividend).

(ii) 18 ÷ 2 = 9,

18 ÷ 3 = 6,

18 ÷ 9 = 2,

18÷ 6 = 3,

18 ÷ 1 = 18,

18 ÷ 18 = 1

If 18 are divided by 2, 3, 9, 6, 1 and 18, it is completely divided.

Thus, 2, 3, 9, 6, 1, 18 or 1, 2, 3, 6, 9 and 18 are the complete divisors or the factors of the multiple 18.

We may define a factor as the multiplier or complete divisor of its multiple.

A multiple has many but limited numbers of factors.

35 have 4 factors, i.e., 1, 5, 7 and 35.

42 have 8 factors, i.e., 1, 2, 3, 6, 7, 14, 21 and 42.

(iii) Let us find the factors of 24.

By division method

24 ÷ 1 = 24

24 ÷ 2 = 12

24 ÷ 3 = 8

24 ÷ 4 = 6

1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24

Taking help of division to check multiples

(i) Is 24 a multiple of 8? Use division.

24 ÷ 8 = 3 (No remainder)

Yes, 24 is a multiple of 8.

(ii) Is 56 a multiple of 5? Use division.

56 ÷ 5

$division to check multiples$

Here remainder is 1

56 is not a multiple of 5 because there is a remainder.

(iii) Is 456 a multiple of 9? Use division.

456 ÷ 9

$check multiples$

Here remainder is 6

456 is not a multiple of 9 because there is a remainder.

Note:

In division if there is no remainder, the dividend is the multiple of the divisor.

Finding the factors of a number through division

(i) Take a look. Is 5 a factor of 15?

15 ÷ 5 = 3 15 ÷ 3 = 5

$Factors of a Number$

No remainder No remainder

5 is factor of 15. 3 is a factor of 15.

Both 3 and 5 are factor of 15.

(ii) Find the factors of 36:

$Factors of 36$

1 × 36 = 36 2 × 18 = 36 3 × 12 = 36

$Find the factors of 36$

4 × 9 = 36 5 is not a factor of 36 6 × 6 = 36

Note:

No need to do any more division because the factors are getting repeated.

Now we can write the factors like this:

The factors of 36 are:

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Note:

It is very important to work systematically in math.

(iii) Is 7 a factor of 24?

24 ÷ 7 = 3 remainder 3

$factor of 24$

Here, remainder = 3

7 is not a factor of 24.

Taking help of division to check multiples

(i) Is 24 a multiple of 8? Use division.

24 ÷ 8 = 3 (No remainder)

Yes, 24 is a multiple of 8.

(ii) Is 56 a multiple of 5? Use division.

56 ÷ 5

$multiple of 5$

Here remainder is 1

56 is not a multiple of 5 because there is a remainder.

(iii) Is 456 a multiple of 9? Use division.

456 ÷ 9

$multiples of 9$

Here remainder is 6

456 is not a multiple of 9 because there is a remainder.

You might like these

Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10
Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:
Divisible by 5 | Test of divisibility by 5| Rules of Divisibility by 5
Divisible by 5 is discussed below: A number is divisible by 5 if its units place is 0 or 5. Consider the following numbers which are divisible by 5, using the test of divisibility by
Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9
A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:
Divisible by 6 | Test of Divisibility by 6| Rules of Divisibility by 6
Divisible by 6 is discussed below: A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42
Divisible by 4 | Test of Divisibility by 4 |Rules of Divisibility by 4
A number is divisible by 4 if the number is formed by its digits in ten’s place and unit’s place (i.e. the last two digits on its extreme right side) is divisible by 4. Consider the following numbers which are divisible by 4 or which are divisible by 4, using the test of
Divisible by 3 | Test of Divisibility by 3 |Rules of Divisibility by 3
A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3. Consider the following numbers to find whether the numbers are divisible or not divisible by 3: (i) 54 Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3.
Relationship between H.C.F. and L.C.M. |Highest Common Factor|Examples
The product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers i.e., H.C.F. × L.C.M. = First number × Second number or, LCM × HCF = Product of two given numbers
Divisibility Rules | Divisibility Test|Divisibility Rules From 2 to 18
To find out factors of larger numbers quickly, we perform divisibility test. There are certain rules to check divisibility of numbers. Divisibility tests of a given number by any of the number 2, 3, 4, 5, 6, 7, 8, 9, 10 can be perform simply by examining the digits of the
Method of H.C.F. |Highest Common Factor|Factorization &Division Method
We will discuss here about the method of h.c.f. (highest common factor). The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers. Let us consider two numbers 16 and 24.
Prime and Composite Numbers | Prime Numbers | Composite Numbers
What are the prime and composite numbers? Prime numbers are those numbers which have only two factors 1 and the number itself. Composite numbers are those numbers which have more than two factors.
Multiples | Multiples of a Number |Common Multiple|First Ten Multiples
What are multiples? ‘The product obtained on multiplying two or more whole numbers is called a multiple of that number or the numbers being multiplied.’ We know that when two numbers are multiplied the result is called the product or the multiple of given numbers.
4th Grade Factors and Multiples Worksheet | Factors & Multiples
In 4th grade factors and multiples worksheet we will find the factors of a number by using multiplication method, find the even and odd numbers, find the prime numbers and composite numbers, find the prime factors, find the common factors, find the HCF(highest common factors
Examples on Multiples | Different Types of Questions on Multiples
Examples on multiples on different types of questions on multiples are discussed here step-by-step. Every number is a multiple of itself. Every number is a multiple of 1. Every multiple of a number is either greater than or equal to the number. Product of two or more numbers
Worksheet on Word Problems on H.C.F. and L.C.M. |Highest Common Factor
In worksheet on word problems on H.C.F. and L.C.M. we will find the greatest common factor of two or more numbers and the least common multiple of two or more numbers and their word problems. I. Find the highest common factor and least common multiple of the following pairs
Word Problems on L.C.M. | L.C.M. Word Problems | Questions on LCM
Let us consider some of the word problems on l.c.m. (least common multiple). 1. Find the lowest number which is exactly divisible by 18 and 24. We find the L.C.M. of 18 and 24 to get the required number.