179 LearnersLast updated on May 26th, 2025
Factors of 403
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 403 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!
What are the factors of 403?
Factors are whole numbers that, when multiplied, the product is equal to 403.
403 is not a prime number, its factors are 1,13,31,403. For every factor, there is a corresponding negative factor, for 403, the negative factors -1, -13, -31, -403.
How to find the factors of 403?
There are various methods we apply to find the factors of any number. Few of them are listed here; multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
Finding Factors Using Multiplication
Step 1: Find all pairs of numbers whose product is 403.
Step 2: All the pairs found represent the factors of 403.
403 is not a prime number. The pair of numbers whose product is 403 is;
1×403=403
13×31 = 403
The factors of 403 are 1,13,31,403.
Finding Factors by Division Method
Step 1: Start by dividing 403 with the smallest number, and check the remainders.
Step 2: 403 is not prime, therefore the divisors it has are 1,13,31,403. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 403 are 1,13,31,403.
Prime factors and prime factorization
— 403 is not a prime number.
— The prime factorization of 403 is 13×31.
— Factors of 403 are 1,13,31,403.
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its factors.
— In the case of 403, only one branch will be extended, as the number is prime factorized as 13×31. 31 is a prime number and cannot be factored further.
Common mistakes and how to avoid them in factors of 403
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 403. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them.
Mistake 1
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Factors of 403 Examples
Problem 1
Find the greatest common factor of 403 and 93.
Find the factors of 403: 1, 13, 31, 403.
Find the factors of 93: 1, 3, 31, 93.
Identify the common factors: 1 and 31.
The greatest common factor is 31.
Explanation
The GCF is the largest number that divides both numbers evenly. By comparing factors, we see that 31 is the biggest common factor of 403 and 93.
Problem 2
Use prime factorization to find the factors of 403.
Begin by dividing 403 by the smallest prime number that divides it, which is 13.
403÷13=31
Both 13 and 31 are prime numbers.
So, the prime factorization of 403 is 13 × 31.
Explanation
Prime factorization breaks down a number into its prime factors. By dividing 403, we find it’s made up of 13 and 31, which are prime. This breakdown also helps confirm the factors we found earlier.
Problem 3
If 13 is one of the factors of 403, what is the other factor?
We know that 13 is a factor, so divide 403 by 13 to find the missing factor. 403÷13=31
The missing factor is 31.
Explanation
When given one factor, divide the original number by that factor to find the other factor in the pair. Here, dividing 403 by 13 gives us 31, confirming that 13 × 31 = 403.
FAQs on Factors of 403
1.What is a prime number that falls after 403?
2. What is the GCF of 403?
3. Is the cube root of 403 rational?
4.Can 403 be divided by 3?
5.What is the cube of 403 ?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 403?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 403 with numbers?
8.What role do numbers and Factors of 403 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 403 skills?
Important Glossaries for Factors of 403
- Factors: numbers that divide the given number without leaving a remainder.
- Prime factorization: breaking numbers down into their prime factors.
- Prime factors: Prime numbers that multiply together to form a given number.
- Composite number: Number that has at least more than one divisor other than 1 and the number itself.
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About BrightChamps in United Arab Emirates
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.
