197 LearnersLast updated on May 26th, 2025
Factors of 103
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 103 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 103?
Numbers or expressions which when multiplied together produce a given number are called factors.
Factors of 103: 1,103
Negative factors of 103 : -1.-103
Prime factorization of 103: 1×103
Sum of factors: 1+103=104
How to find the factors of 103?
Few of the methods to find the factors 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 a and b such that a multiplied by b equals 103.
Step 2: All the pairs found represent the factors of 103.
103 is a prime number.
The factors of 103 are 1,103.
Finding Factors by Division Method
Step 1: Start by dividing 103 with the smallest number, and check the remainders.
Step 2: Divisors of 103 are 1 and 103. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 103 are 1,103.
Prime Factors and Prime Factorization
— 103 is a prime number.
— The prime factorization of 103 is 103 only.
— Factors of 103 are 1,103
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its prime factors.
— In case of 103, only one branch will be extended, as there are no other factors of the number.
. Factor pairs
Combination of two numbers, a and b whose product is equal to 103. a and b are a factor pair of 103.
The factor pairs of 103 are
Positive factor pairs - (1,103)
Negative factor pairs - (-1,-103)
Common mistakes and how to avoid them in the factors of 103
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 103. 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
All positive factors have a counter factor that is negative. Oftentimes, the negative factors are not included.
Factors of 103 Examples
Problem 1
Is 103 divisible by 3? Explain why or why not.
Try dividing 103 by 3: 103÷3=34.3333…
Since 103 divided by 3 does not give a whole number (it gives a decimal), 3 is not a factor of 103.
Explanation
For a number to be a factor, it must divide the original number evenly without leaving a remainder or decimal.
Problem 2
Prove that 103 is a prime number by checking if any numbers other than 1 and 103 divide into it.
To check if 103 is prime, divide it by all whole numbers from 2 up to 103≈10:
103 ÷ 2 = 51.5 → Not a factor.
103 ÷ 3 = 34.333… → Not a factor.
103 ÷ 5 = 20.6 → Not a factor.
103 ÷ 7 = 14.71 → Not a factor.
103 ÷ 9 = 11.44 → Not a factor.
None of these divisions result in a whole number, which means no numbers other than 1 and 103 divide it evenly. Therefore, 103 is a prime number.
Explanation
By testing smaller numbers, we can confirm that no other numbers (other than 1 and 103) divide into 103 evenly.
Problem 3
A group of 103 students wants to arrange themselves in equal rows for a school assembly. Can they form rows of equal size, other than 1 row of 103 or 103 rows of 1?
Check if 103 has any factors other than 1 and 103.
Since 103 is prime, its only factors are 1 and 103.
The group of students can only be arranged in:
1 row of 103 students or
103 rows of 1 student.
Explanation
Because 103 is prime, it doesn’t have factors that allow it to be divided into rows of equal size (other than 1 row or 103 rows). This problem helps us see how knowing factors can be helpful for arranging groups evenly.
FAQs on Factors of 103
1.What can be multiplied to get 103?
2.What are the multiples of 103?
3. What is the cube of 103?
4.Is 103 a twin prime?
5. Is 103 a perfect square?
Important Glossaries for Factors of 103
Factors: Numbers or expressions which when multiplied together produce a given number
Prime factorization: Breaking numbers down into their prime factors.
Prime number: A number with two factors and one of them is one
Composite number: Number that exceeded having just 2 divisors.
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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.
