**Factors Of 100**

**What is Factors ?**

**When two or more numbers are multiplied together to give a product, each is called a factor of the product. The product of two or more numbers is said to be a multiple of each of those numbers.**

**For example 4 x 5 = 20. Here 4 and 5 are factors of 20 and 20 is a multiple of both 4 and 5.**

**OR**

**A number which divides the given number exactly ( without leaving any remainder ) is called a factor of given number.**

**Comparison Of Factors and Multiple**

Factors |
Multiples |

Every number is a factor of itself. | Every number is a multiple of itself. |

1 is a factor of every number. | 1 is a multiple of 1 only. |

The factors of a number are countable. | The multiple of a number are its uncountable. |

Every factor of a number other than the number itself is less than the number. | Every multiple of a number other than the number itself is greater than the number. |

**Factor :-**

**When two or more numbers are multiplied to give a product, each number is called a factor of the product. Here are the first eleven whole numbers and their factors:**

Whole Numbers |
Factors |

0 | 0,1,2,3,4,5,6,7,8,9………. |

1 | 1 |

2 | 1,2 |

3 | 1,3 |

4 | 1,2,4 |

5 | 1,5 |

6 | 1,2,3,6 |

7 | 1,7 |

8 | 1,2,4,8 |

9 | 1,3,9 |

10 | 1,2,5,10 |

**Thus, a number (called divisor) is a factor of another number (called dividend) if it divides the dividend exactly, ie there is no remainder left over.**

**For example 3 is a factor of 36, but 3 is not a factor of 43.**

**PRIME FACTORIZATION**

**A prime number has two factors : itself and 1 while a composite number has more than two factors.**

**The multiplication facts of 32 are as follows:**

32 = 2x1x16

=2 x 1 x 2 x 2 x 2 x 2

= 2x2x2x2 x 2 x1

**Usually we do not write the factor 1 as it is understood. Factors of 32 are thus 2, 2, 2, 2 and 2. Since all the 5 numbers are prime numbers these are called the prime factors of 32. We also note that a single prime number is repeated in the prime factorization of 32.**

**Example : Give the prime factorization of 36.**

Start dividing 36 step by step by the prime numbers in order. First of all divide it by 2 as many times as possible. Thus,

**36** = **2 x 18 **

** = 2x2x9**

** = 2x2x3x3**

**Thus, the prime factors of 36 are 2,2,3,3.**

**Example** : **Find the prime factors of 64.**

** Use repeated division by prime numbers as it is the easiest way to get prime factors.**

**Factors Of 100**

The** Factors of 100** are the number that produce the** result as 100** when two numbers are multiplied together.

**Factors of 100** are the whole numbers **which could be either positive or negative** but not a fraction or decimal number. **To find the factors of a number, 100 , we will use the factorization method.**

**factors of 100**

**2, 4 , 5 , 10 , 20 , 25 , 50 , 100**

Pair Factors | Prime Factorization |

1×100 | 2×2×5×5 |

2×50 | 2^{2} ×5^{2} |

4×25 | |

5×20 | |

10×10 |

**In Factorization Method . first consider the number s. 1 and 75 and continue with finding the other pair of multiples of 75 , which gives the result as an original number.**

### Pair Factors Of 100

1×100 = 100 ,then ( 1 , 100 ) is a pair factor of 100

2×50 = 100 , then (2, 50 ) is a pair factor of 100 ** { ∵ 25 = 5×5×2 }**

4×25 = 100 .then ( 4,25) is a pair of 100 **{ ∵ 25 = 5×5 }**

5×20 = 100 .then ( 5,20 ) is a pair of 100 **{ ∵ 20 = 5×4 }**

10×10 = 100 .then ( 10,10) is a pair of 100 **{ ∵ 10 = 2×5 }**

**The positive pair factor of 100 are ( 1 , 100 ) , ( 2,50 ) and ( 4,25) , ( 5, 20 ) and ( 10 , 10 )**

### Now we find the negative pair of factors , the proceed with following steps

### Pair Factors Of 100

-1×-100 = 100 ,then ( -1 , -100 ) is a pair factor of 100

-2×-50 = 100 , then (-2, -50 ) is a pair factor of 100 ** **

-4×-25 = 100 .then ( -4,-25) is a pair of 100

-5×-20 = 100 .then ( -5,-20 ) is a pair of 100

-10×-10 = 100 .then ( -10,-10) is a pair of 100

**The positive pair factor of 100 are ( -1 , -100 ) , ( -2, -50 ) and ( -4, -25) , ( -5, -20 ) and ( -10 , -10 )**

**Now we calculate the Factors of 100?**

**Following steps to calculate the factors of a number.**

First, write the number 100.

Find the two numbers, which gives the result as 10 under the multiplication, 5 and 20, such as 5 x 20 = 100.

We know that 5 is a prime number which has only two factors, i.e., 1 and the number itself( 1 and 5).

5 = 5 x 1

But look at the number 25, which is a composite number but not a prime number. So it can be further factorized

20 = 2 x 2 x 5 x 5 x 1

Therefore, the factorization of 100 is written as, 100 = 2 x 2 x 5 x 5 x 1..

Finally, write down all the unique numbers (i.e.) 2 x 2 x 5 x 5 x 1

Factors Of 100 |

1 , 2 , 4 , 5 , 10 , 20 , 25 , 50 and 100 |

### Prime Factors Of 100 BY Using Division Method

**First Step :- ****Divide the number 100 with the smallest prime factor , say2 .**

**= ****100 ÷2 = 50**

**Second Step :- Again divide 100 by 2 and the process goes on.**

**= 50÷2 =25**

**Third Step :- If we divide 25 by 2 we will get a fractional number ,which cannot be a factor. Say 5**

**25 ÷ 5 =5**

**5 ÷ 5 =1**

**Fourth step :-Finally we received the number 1 at the end of the division process .**

** Now we received prime factors of100 are 2 × 2 × 5 × 5 OR 2 ^{2} ×5^{2}**

**Tan 30 degrees**

**What is the prime factorization of 75**

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