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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
1.  What Are the Factors of 105? 
2.  How to Calculate the Factors of 105? 
3.  Factors of 105 by Prime Factorization 
4.  Factors of 105 in Pairs 
5.  FAQs on Factors of 105 
What Are the Factors of 105?
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.
How to Calculate the Factors of 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.
Factors of 105 by Prime Factorization
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.
Factors of 105 in Pairs
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.
Tips and Tricks:
 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.
Factors of 105 Solved Examples

Example 1: 105 students are to be divided into groups such that there are an equal number of students in each group. In how many ways can they be grouped?
Solution:
We will use the concept of factor pairing to divide 105 students into groups.
We know that (35, 3), (5, 21), and (7, 15) are the factor pairs of 105.
Thus, the students can be grouped in three different ways.

Example 2: Emily has a chocolate box with 105 chocolates in it. She distributed the chocolates among her classmates. Can you find the total number of students if she gives 5 chocolate to each one of them?
Solution:
Given, total number of chocolates = 105
Chocolates given to each student = 5
Thus, the number of students in the class is = 105 ÷ 5 = 21 students.
Here we can see the numbers used, i.e. (5,21), is a pair factor of 105.

Example 3: Is there any chance that you can divide 105 geometry boxes equally among 50 kids?
Solution: Clearly, the answer is NO! Because 50 is not a factor of 105 and leaves a remainder, so we cannot distribute 105 geometry boxes to 50 kids equally.
FAQs on Factors of 105
What are the Factors of 105?
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105 and its negative factors are 1, 3, 5, 7, 15, 21, 35, 105.
How Many Factors of 105 are also Factors of 3?
Since, the factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105 and the factors of 3 are 1, 3.
Hence, [1, 3] are the common factors of 105 and 3.
What is the Sum of all the Factors of 105?
Sum of all factors of 105 = (3^{1 + 1}  1)/(3  1) × (5^{1 + 1}  1)/(5  1) × (7^{1 + 1}  1)/(7  1) = 192
What is the Greatest Common Factor of 105 and 97?
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105 and the factors of 97 are 1, 97. 105 and 97 have only one common factor which is 1. This implies that 105 and 97 are coprime.
Hence, the Greatest Common Factor (GCF) of 105 and 97 is 1.
What are the Pair Factors of 105?
The pair factors of 105 are (1, 105), (3, 35), (5, 21), (7, 15).
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