126 LearnersLast updated on May 26th, 2025
Factors of 1965
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1965, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1965?
The numbers that divide 1965 evenly are known as factors of 1965.
A factor of 1965 is a number that divides the number without remainder.
The factors of 1965 are 1, 3, 5, 15, 131, 393, 655, and 1965.
Negative factors of 1965: -1, -3, -5, -15, -131, -393, -655, and -1965.
Prime factors of 1965: 3, 5, and 131.
Prime factorization of 1965: 3 × 5 × 131.
The sum of factors of 1965: 1 + 3 + 5 + 15 + 131 + 393 + 655 + 1965 = 3168
How to Find Factors of 1965?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1965. Identifying the numbers which are multiplied to get the number 1965 is the multiplication method.
Step 1: Multiply 1965 by 1, 1965 × 1 = 1965.
Step 2: Check for other numbers that give 1965 after multiplying
3 × 655 = 1965
5 × 393 = 1965
15 × 131 = 1965
Therefore, the positive factor pairs of 1965 are: (1, 1965), (3, 655), (5, 393), (15, 131).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1965 by 1, 1965 ÷ 1 = 1965.
Step 2: Continue dividing 1965 by the numbers until the remainder becomes 0.
1965 ÷ 1 = 1965
1965 ÷ 3 = 655
1965 ÷ 5 = 393
1965 ÷ 15 = 131
Therefore, the factors of 1965 are: 1, 3, 5, 15, 131, 393, 655, 1965.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1965 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1965 ÷ 3 = 655
655 ÷ 5 = 131
131 ÷ 131 = 1
The prime factors of 1965 are 3, 5, and 131.
The prime factorization of 1965 is: 3 × 5 × 131.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1965 is divided by 3 to get 655.
Step 2: Now divide 655 by 5 to get 131.
Step 3: Divide 131 by 131 to get 1. Here, 131 is a prime number, that cannot be divided anymore. So, the prime factorization of 1965 is: 3 × 5 × 131.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1965: (1, 1965), (3, 655), (5, 393), and (15, 131).
Negative factor pairs of 1965: (-1, -1965), (-3, -655), (-5, -393), and (-15, -131).
Common Mistakes and How to Avoid Them in Factors of 1965
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1965, 1 and 1965 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of 1965 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1965/1.5 = 1310, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1965 are prime numbers.
For example, 3, 5, and 131 are the prime factors of 1965, but it has other factors like 15, 393.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1965 as 3 × 5 × 131 and missing all the key factors.
Factors of 1965 Examples
Problem 1
There are 3 teams and 1965 fans. How will they be divided equally among the teams?
Each team will have 655 fans.
Explanation
To divide the fans equally, we need to divide the total fans with the number of teams.
1965/3 = 655
Problem 2
A page is filled with 1965 words, and there are 5 columns. How many words are in each column?
393 words.
Explanation
To find the number of words in each column, we use the formula,
Total words = number of columns × words in each column
1965 = 5 × words in each column
To find the value of words in each column, we need to divide by 5.
1965/5 = words in each column
Words in each column = 393.
Problem 3
There are 15 buses and 1965 passengers. How many passengers will be in each bus?
Each bus will have 131 passengers.
Explanation
To find the passengers in each bus, divide the total passengers with the number of buses.
1965/15 = 131
Problem 4
In a stadium, there are 1965 seats, and 5 sections. How many seats are there in each section?
There are 393 seats in each section.
Explanation
Dividing the seats with the total sections, we will get the number of seats in each section.
1965/5 = 393
Problem 5
1965 pages need to be distributed among 15 binders. How many pages will go in each binder?
Each of the binders has 131 pages.
Explanation
Divide total pages with binders.
1965/15 = 131
FAQs on Factors of 1965
1.What are the factors of 1965?
2.Mention the prime factors of 1965.
3.Is 1965 a multiple of 15?
4.Mention the factor pairs of 1965.
5.What is the square of 1965?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 1965?
7.What are some fun ways kids in Vietnam can practice Factors of 1965 with numbers?
8.What role do numbers and Factors of 1965 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 1965 skills?
Important Glossaries for Factors of 1965
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1965 are 1, 3, 5, 15, 131, 393, 655, and 1965.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 131 are prime factors of 1965.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1965 are (1, 1965), (3, 655), etc.
- Prime factorization: Breaking down a number into its prime factor components. The prime factorization of 1965 is 3 × 5 × 131.
- Negative factors: Factors that are negative numbers, such as -1, -3, -5, etc., for 1965.
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About BrightChamps in Vietnam
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.
