Factors of 105

Factors of 105 are the list of integers that can be evenly divided into 105. There are overall 8 factors of 105 among which 105 is the biggest factor and 1, 3, 5, 7, 15, 21, 35, and 105 are positive factors. The sum of all factors of 105 is 192 and its factors in Pairs are (1, 105), (3, 35), (5, 21), and (7, 15).

• Factors of 105: 1, 3, 5, 7, 15, 21, 35 and 105
• Negative Factors of 105: -1, -3, -5, -7, -15, -21, -35 and -105
• Prime Factors of 105: 3, 5, 7
• Prime Factorization of 105: 3 × 5 × 7 = 3 × 5 × 7
• Sum of Factors of 105: 192

Factors of 105 are the numbers that divide 105 perfectly without leaving any remainder.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.

To calculate the factors of 105, we can use the division method. Let's start with 1.

105 ÷ 1 leaves remainder 0.

Since 105 is not an even number, 2 does not divide 105 completely. Thus, it leaves a remainder.

105 ÷ 3 leaves remainder 0. 

105 ÷ 5 leaves remainder 0.

105 ÷ 7 leaves remainder 0.

105 ÷ 15 leaves remainder 0.

105 ÷ 21 leaves remainder 0.

105÷ 35 leaves remainder 0.

105 ÷ 105 leaves remainder 0.

Thus, the factors of 105 that we have obtained are 1, 3, 5, 7, 15, 21, 35, and 105.

Explore factors using illustrations and interactive examples

• Factors of 75: The factors of 75 are 1, 3, 5, 15, 25 and 75
• Factors of 175: The factors of 15 are 1, 3, 5, and 15. 
• Factors of 35:  The factors of 35 are 1, 5, 7, and 35.
• Factors of 70: The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
• Factors of 42: The factors of 1, 2, 3, 6, 7, 14, 21, and 42.

Prime factorization means expressing a composite number as the product of its prime factors. 

Prime factorization of 105 = 3 × 5 × 7. We can determine the other composite factors of 105 from its prime factors. We can see that 35 is a factor of 105. Similarly, 15 and 21 are also factors of 105.

The pair of numbers that give 105 on multiplication are the factors of 105 in pairs. Look at the rainbow below. We start from 1 and move forward by including the numbers that give us 105 as their product.

We get the following combinations: 1 × 105, 3 × 35, 5 × 21, and 7 × 15.

• All the numbers have at least two factors. 105 will have the first factor as 1 and the other factor is 105 itself.
• Factors of 105 are all the possible numbers 105 is divisible by. They may be prime numbers or composite numbers.
• Factors are always integers. They can never be fractions or decimals.