280 LearnersLast updated on May 26th, 2025
Factors of 105
Do you know how number tricks work? Most of the number tricks work because of the unique characteristics of each number, i.e., factors. A factor of a number is any number that can evenly divide the number. For distributing objects, we use factors in our daily life.
What are the 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
How to find the factors of 105
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
Finding factors using multiplication method:
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).
Finding factors by division method
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 factors and prime factorization
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.
Factor tree
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).
Common mistakes and how to avoid them in factors of 105
While finding the factors of any numbers, students tend to make mistakes. Mostly they tend to repeat the same error. Here is a list of some common mistakes and the ways to avoid them.
Mistake 1
Errors in division
Kids tend to make errors in division, to avoid it we need to recheck the calculations. And we need to verify the answer
Factors of 105 examples
Problem 1
In a class there are 105 students, for an activity teacher wants to divide the class equally. Which are the possible ways to divide the class.
There are three possible ways to divide. They are (3, 35), (5, 21), (7, 15)
Explanation
To divide a class of students into groups, we need to consider the factors of total number of students. Here there are factors of 105, factors are (3, 35), (5, 21), (7, 15).
Problem 2
If we divide 105 chocolates among 21 students. How many chocolates did each student get?
5 chocolates
Each of the students can get 5 chocolates
Explanation
To find the number of chocolates each student can get, we need to divide the total number of chocolates with the number of students. That is 105 ÷ 21 = 5.
Problem 3
List out all the factor pairs of 105
The factor pairs of 105 are (1, 105), (3, 35), (5, 21), (7, 15).
Explanation
The pair of numbers whose product is 105 is the factor pair of 105. Here, 1 × 105 = 105; 3 × 35 = 105; 5 × 21 = 105; 7 × 15 = 105.
Problem 4
Find the common factors of 105 and 140
1, 5, 7, 35 are the common factors of 105 and 140
Explanation
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Therefore, the common factors are 1, 5, 7, 35
FAQs on factors of 105
1.What is the factor tree for 105?
2.What two numbers make 105?
3.What are five factors of 105?
4.What are the multiples of 105?
5.Is 105 a multiple of 7?
6.How can children in United States use numbers in everyday life to understand Factors of 105?
7.What are some fun ways kids in United States can practice Factors of 105 with numbers?
8.What role do numbers and Factors of 105 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 105 skills?
Important glossaries for factors of 105
- 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.
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About BrightChamps in United States
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
