# 5th Class Mathematics Factors and Multiples Factors

## Factors

Category : 5th Class

### Factors

Factors of a number, divide the number completely.

If a, b, c, d __ are factors of "m" then 'm will be completely divisible by a, b, c, d__.

How to Get Factors of a Number

Factors of a number can be found by hit and trial method. Get any number, if it divides completely the number whose factor is to be found, it is a factor of that number. Let us discuss some rules of divisibility in order to easily find the factors of a number.

Rules of divisibility

(a) The numbers which have 0, 2, 4, 6, or 8 at the unit place is divisible by 2. For example: 24434, 21450, 231545452218 are divisible by 2.

(c) If sum of digits of a number is divisible by 3 then the number is divisible by 3. For example: Sum of the digits of 276 = 2 + 7 + 6 = 15. 15 is divisible by 3, therefore, 276 is divisible by 3.

(d) If the number formed by two digits from right side of a number is divisible by 4 the number is divisible by 4. For example: 28 in 5428 is divisible by 4, therefore, 5428 is divisible by 4

(e) If a number has the digit 0 or 5 at unit place, the number is divisible by 5. For example: 0 is at the unit place in the number 5450, therefore, .5450 is divisible by 5.

(f) If an even number is divisible by 3 then the number is divisible by 6. For example: 558 is an even number and divisible by 3, therefore, 558 is divisible by 6

(g) If the number formed by three digits from right side of a number is divisible by 8 then the number is divisible by 8. For example: 248 in 56248 is divisible by 8, thus 56248 is divisible by 8.

(h) If sum of digits of a number is divisible by 9, the number is divisible by 9. For example: Sum of digits of 5689485 = 5 + 6 + 8 + 9 + 4 + 8 + 5 = 45 and 45 is the divisible by 9. Thus 9689485 is divisible by 9.

(i) If a number has the digit 0 at the unit place, the number is divisible by 10. For example: 0 is at the unit place in the number 4560, 4560 is divisible by 10.

(j) If difference of the sum of the alternate digits of a number is either 0 or divisible by 11, the number is divisible by 11. For example: Difference of the sum of the alternative digits of 5478693 = (5+7+6+3)-(4+8+9) = 0 Thus 5478693 is divisible by 11.

(k) If a number has two prime factors then product of the prime factors is also a factor of the number. For example: 3 and 5 are the prime-factors 2445 thus 15 is also a factor of 2445.

Find the factors of 10.

By hit and trial method we get the numbers 1, 2, 5, and 10 which divide 10 completely.

How many factors are there of 56?

Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56. So there are 8 factors of 56.

Is 8 a factor of 45684?

The number formed by the three digits from right side is 684 and 684 is not divisible by 8. Therefore, 8 is not a factor of 45684.

What least number should be subtracted from 16639 so that 24 becomes factor of it?

Solution:

Divide 16639 by 24, the remainder you will get, should be subtracted from 16639 so that 24 becomes factor of it.

24)\frac{693}{\begin{align} & 16639 \\ & \frac{144}{0223} \\ & \frac{-216}{0079} \\ & \frac{-72\,\,\,}{07} \\ \end{align}}(

Prime Numbers

The numbers which have only two factors, 1 and the number itself are called prime  numbers.

Factors of 2 = 1, 2

Factors of 3 = 1, 3

Factors of 5 = 1, 5

Factors of 19 = 1, 19

We see all the above numbers 2, 3, 5, and 19 has only two factors 1 and the number itself. Therefore, all the above numbers are prime numbers.

Twin Primes

Two consecutive prime numbers with the difference 2 are called twin primes.

Some pairs of twin primes are the following:

Pairs of twin primes: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31)

Prime Triplets

Prime triplet is a set of three prime numbers which consists of a pair of twin primes and one other prime number which differs from one of the numbers of twin primes by 4 and 6 from other. There are two forms of prime triplet (p, p + 2, p + 6) and (p, p + 4, p + 6) where p is a prime number. In the (p, p + 2, p + 6) form of prime triplet p and p + 2 is a pair of twin primes. In the (p, p + 4, p + 6) form of prime triplet p + 4 and p + 6 is a pair of twin primes. (2, 3, 5) and (3, 5, 7) are two exceptions of prime triplet.

Some sets of prime triplet are the following:

(5, 7, 11), (7, 11, 13), (11, 13, 17), (13, 17, 19), (17, 19, 23), (37, 41, 43), (41, 43, 47)

Composite Numbers

A number which has more than two factors is called a composite number.

Factors of 4 = 1, 2, 4

Factors of 6 = 1, 2, 3, 6

Factors of 9 = 1, 3, 9

All the above numbers 4, 6, and 9 have more than two factors. Therefore, these are composite numbers.

Perfect Numbers

If sum of all the factors of a number is twice of the number, the number is called a perfect number.

Factors of 6 = 1, 2, 3, 6

Sum of factors =1+2+3+6= 12

Sum of factors = 2 x the number. Therefore, 6 is a perfect number.

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