Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 3 teams and 1965 fans. How will they be divided equally among the teams?
Each team will have 655 fans.
To divide the fans equally, we need to divide the total fans with the number of teams.
1965/3 = 655
A page is filled with 1965 words, and there are 5 columns. How many words are in each column?
393 words.
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.
There are 15 buses and 1965 passengers. How many passengers will be in each bus?
Each bus will have 131 passengers.
To find the passengers in each bus, divide the total passengers with the number of buses.
1965/15 = 131
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.
Dividing the seats with the total sections, we will get the number of seats in each section.
1965/5 = 393
1965 pages need to be distributed among 15 binders. How many pages will go in each binder?
Each of the binders has 131 pages.
Divide total pages with binders.
1965/15 = 131
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.
: She loves to read number jokes and games.