Last updated on May 26th, 2025
The numbers that can be divided by another number without leaving a remainder are known as factors of 963. In our daily lives, factors play a significant role in simplifying fractions, event planning, packing products, transportation, and splitting components like books, products, people, funds, and workloads into equal quantities. In this article, we will learn more about factors and their applications.
Factors are numbers that combine through multiplication to give the original number as the result.
For example:
963× 1 = 963
321 × 3 = 963
107 × 9 = 963 … and so on.
Factors of 963 are 1, 3, 9, 107, 321, and 963. These numbers divide 963 without leaving a remainder. Along with positive factors, there will also be corresponding negative factors.
Negative Factors of 963: -1, -3, -9, -107, -321, -963.
Prime Factors of 963: 3 and 107.
Prime factorization of 963: 32 × 107.
Sum of Factors of 963: 1 + 3 + 9 + 107 + 321 + 963 = 1404.
Identifying the factors of 963 is useful in different scenarios, and it helps to break down the number into smaller and more manageable parts, making it easier to understand. Here are the important methods that you can find the factors of 963:
The multiplication method involves finding the pairs of numbers that multiply together to give the original number. For example: 1 × 963 = 963, so here both 1 and 963 are the factors of 963.
To find all the pairs of numbers that multiply to give 963, here are the steps to follow.
Step 1: All the numbers are divisible by 1 and the number itself, so start with 1 and the number itself,
1 × 963 = 963
And the factors are 1 and 963.
Step 2: Now check divisibility by 2, 3, 4, 5, etc.
Start with smaller numbers 2, 3, and so on. Stop checking once you reach the square root of 963, (which is approximately 31). Any factor larger than the square root of 963 will have a corresponding smaller factor, so checking the divisibility up to 31 is needed.
Check divisibility by 3: To check if 963 is divisible by 3, we need to sum the digits of 963:
9 + 6 + 3 = 18, where 18 is divisible by 3. So, 963 is divisible by 3.
963 ÷ 3 = 321
And the factors are 3 and 321.
Check divisibility by 9: To check if 963 is divisible by 9, we need to sum the digits of 963 again: 9 + 6 + 3 = 18, and 18 is divisible by 9. Now we divide 963 by 9:
963 ÷ 9 = 107
And the factors are 9 and 107.
Step 3: From the steps we have done above, the factors of pairs of 963 are:
1 × 963, 3 × 321, 9 × 107
The factors of 963, which we get through the multiplication method, are:
1, 3, 9, 107, 321, and 963.
The division method involves finding the factors that divide a number by smaller numbers, which ones divide it evenly. If the result is an integer, then both the divisor and the quotient are factors of the number.
Step 1: Divide 963 by 1 – 963 ÷ 1 = 963.
Step 2: Divide 963 by 3 – 963 ÷ 3 = 321.
Step 3: Divide 963 by 9– 963 ÷9 = 107.
The whole step shows that all the numbers divide 963 evenly, and the factors are
1, 3, 9, 107, 321, 963
Prime factors are prime numbers that divide the given number evenly without leaving a remainder.
Prime factorization is a process of expressing numbers into its prime factors that, when multiplied together, give the original number.
Prime Factors of 963: Prime factors of 963 are 3 and 107.
There are 2 common methods to find the prime factors of a number and they are:
Prime Factorization of 963: Prime factorization is the process of expressing numbers to prime factors by breaking them. Here is the step-by-step solution for 963:
The prime factorization of 963 is:
963 = 3 x 3 x107 or 32 x 107
A factor tree visually depicts how a number breaks down into its prime factors. This process involves step-by-step, beginning with the smallest prime number and continuing until only prime factors remain, as shown below.
Step 1: Start with 963:
Select two factors of 963, which is 3 and 321.
Step 2: Factors of 321:
321 = 3 × 107
Step 3: Now check 107:
107 is a prime number, so it cannot be factored further.
Factor pairs are two numbers that, when multiplied together, produce the original number. Each pair includes one number that divides the original number evenly and the resulting quotient.
Positive pair factors: (1, 963), (3, 321), (9, 107)
Negative pair factors: (−1, −963), (−3, −321), (−9, −107)
Commonly, kids make mistakes while doing factors of 963. Here, let’s learn about some common problems of factors of 963. Some common mistakes and solutions are given below:
Emily has 963 books to divide evenly into multiple boxes for a charity event. For that, she can ensure the same number of books in each box. So, what will be the total number of boxes she can use?
Emily can arrange the book using any of the factors of 963 into boxes.
To split the books equally, the number of boxes must be a factor of 963. Each factor shows the possible number of boxes she could use. Thus, Emily has the following choices:
All 963 books will fit in one box if she utilizes one.
James wanted to build a rectangular garden with 963 square tiles. For the garden's area to be precisely 963 square units, he wants its length and width to be factors of 963. What possible sizes could the garden have?
The possible dimensions of the garden are given by the factor pairs of 963:
(1,963), (3,321), (9,107)
The area of the garden is 963 square units, so the length and width must be a factor of 963.
so the measurement could be 1 unit by 963 units, 3 units by 321 units, and 9 units by 107 units.
A baker has 963 cookies, and she wants to have them in equal batches. How many batches of cookies can she make, and how many will fit in each batch?
The possible numbers of batches the baker can make are the factors of 963, and the number of cookies in each batch will be the quotient of 963 ÷ factor.
The number of batches is a factor of 963 to divide 963 cookies into equal batches. The baker can divide the cookies equally for each factor:
1×963
3×321
9×107
107×9
321×3
963×1
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.