Factors and Multiples
Category : 5th Class
Factors and Multiples
Introduction
We have studied about the operations on numbers. Now, we will study two important terms that is, 'factors' and 'multiples'. They are related to the operations of multiplication and division.
Factors
Factors of a number is the number, which divides the given number completely.
If a, b, c, d.... are factors of 'm' then 'm' will be exactly divisible by a, b, c, d....
How to Get Factors of a Number
To find all possible factors of a number, we have to find all the numbers, which divide the given number exactly.
Rules of Divisibility
Find all the possible factors of 15.
Solution: 1, 3, 5, 15 are factors of 15.
Find all the possible factors of 56.
Solution: 1, 2, 4, 7, 8, 14, 28, 56 are factors of 56.
Is 3 a factor of 4665366564?
Solution:
Yes.
Sum of digits of given number
\[=4+6+6+5+3+6+6+5+6+4=51\] and 51 is divisible by 3.
Prime Number
The numbers which have only two factors, land the number itself are called prime numbers.
For example:
Factors of 5 = 1, 5
Factors of 7 = 1, 7
Factors of 11= 1, 11
Therefore, 5, 7, and 11 are prime numbers.
Twin Primes
Two consecutive prime numbers with the difference of 2 are called twin primes.
Write two pairs of twin primes.
Solution:
(3, 5), (5, 7) as 3, 5 and 7 are prime numbers and the two pairs of numbers have a difference of 2.
Composite Number
A number which has more than two factors is called a composite number.
Factors of 6 = 1, 2, 3, 6
Factors of 14 = 1, 2, 7, 14
Therefore, 6 and 14 are composite numbers
Perfect Number
If sum of all the factors of a number is twice of the number, the number is called a perfect number.
6 is a perfect number because sum of factors of\[6=1+2+3+6=12\]
Common Factors
The same factors of two or more than two different numbers are called common factors.
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 16 = 1, 2, 4, 8, 16
1, 2, 4 are the common factors of 12 and 16
Co-prime or Relatively Prime Numbers
If two numbers have only one common factor that is the numbers are called co-prime or relatively prime numbers.
Factors of 8 = 1, 2, 4, 8
Factors of 9 = 1, 3, 9
1 is the only common factor of 8 and 9. Therefore, 8 and 9 are relatively co-prime numbers.
Multiples
When two or more than two numbers are multiplied with each other, the resulting number is the multiple of all that numbers. Like if\[A\times B=C\], C is multiple of both A and B.
Multiples of 7 = 7, 14, 21, 28, 35, .......
Multiples of 8 = 8, 16, 24, 32, 40, ......
Common Multiples
The same multiples of two or more than two different numbers are called common multiples.
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, .....
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, .....
Common multiples of 6 and 4 = 12, 24, 36 etc.
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, ....
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ....
Common multiples of 5 and 6 = 30, 60, .....
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