Factors of 105

The numbers which can evenly divide 105 are the factors of 105. 1, 3, 5, 7, 15, 21, 35, 105 are the factors of 105.

Negative factors of 105: The negative factors of 105 are the negative counterparts of the positive factors. -1, -3, -5, -7, -15, -21, -35, -105 are the negative factors of 105.

Prime factors of 105: A prime number is a number which has only two factors, i.e., 1 and the number itself.
3, 5, 7 are the prime factors of 105.

Prime factorization of 105: The process of splitting a number into smaller prime numbers is prime factorization. Here, the product of prime numbers is the number itself.

The prime factorization of 105 is 3¹ × 5¹ × 7¹
 

Factors of a number is a number which can evenly divide the number. Some methods which are used to find the factor of a 105 are,

• Multiplication method

• Division method

• Prime factors and prime factorization

• Factor tree
   

In the multiplication method a pair of numbers are identified, the product of multiplying the number is 105. 

Step 1: Find the numbers whose product is 105.

1 × 105 = 105

3 × 35 = 105

5 × 21 = 105

7 × 15 = 105

Step 2: List them as pairs

The pair of factors are (1, 105), (3, 35), (5, 21), (7, 15).
 

In the division method, we need to check which number can evenly divide 105. 

Let’s check the factors of 105 using division method

105 ÷ 1 = 105

105 ÷ 3 = 35

105 ÷ 5 = 21

105 ÷ 7 =15

So, the factors are 1, 3, 5, 7, 15, 21, 35, and 105.
 

Prime numbers are the numbers which have only two factors. The process of breaking down a large number into a smaller prime number is prime factorization. 

To find the factors of a number prime factorization, we need to follow these steps

Step 1: The given number needs to be divided with the smallest prime number.

Step 2: Now, we need to divide the remainder in step 1 with the prime number. The process is continued till the remainder is a prime number.

 
 Let's use the prime factorization method to find the factors of 105.

The prime factors of 105 are 3, 5, 7.

2, 3, 5, 7, 11, 13, 17,… are the prime numbers. 

 
Step 1: Checking the divisibility by 2: 105 is an odd number, so, not divisible by 2.

Checking the divisibility by 3: 105 ÷ 3 = 35.

Step 2: Now, the remainder is 35. 

Checking the divisibility by 3: 35 is not divisible by 3

Checking the divisibility by 5: 35 ÷ 5 = 7.

Step 3: Now, the remainder is 7 which is a prime number. 

So, the factors of 105 are 1, 3, 5, 7, 105.
 

The Pictorial representation of factors of a number. It is in the form of a tree where the given number is split into branches which represent all the factors. 

The factor tree of 105:
 

105
  / \
3   35
      / \
     5   7

Factor pair: A pair of factors of a number. The product of those numbers is the number itself. Factor pairs can be both positive and negative.

Positive pair factors: (1, 105), (3, 35), (5, 21), (7, 15).

Negative pair factors: (-1, -105), (-3, -35), (-5, -21), (-7, -15).

• Prime number: Any numbers which has only two factors are the prime numbers

• Composite numbers: The number which has more than two factors

• Remainder: The value left after dividing a number by another number. For example, 1 is the remainder when we divide 5 by 2.

• Product: The product of any number is the result of multiplying the number.