262 LearnersLast updated on May 26th, 2025
Factors of 1009
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 1009 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 1009?
Factors are whole numbers that, when multiplied, the product is equal to 1009.
1009 is a prime number, its only factors are 1 and 1009. For every factor, there is a corresponding negative factor, for 1009, the negative factors -1, -1009.
How to find the factors of 1009?
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 1009.
Step 2: All the pairs found represent the factors of 1009.
1009 is a prime number. The only pair of numbers whose product is 1009 is 1×1009=1009.
The factors of 1009 are 1 and 1009 only.
Finding Factors by Division Method
Step 1: Start by dividing 1009 with the smallest number, and check the remainders.
Step 2: 1009 is prime, therefore the only divisors it has are 1 and 1009. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 1009 are 1 and 1009 only.
Prime factors and prime factorization
— 1009 is a prime number.
— The prime factorization of 1009 is 1009 times 1.
— Factors of 1009 are 1,1009
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its factors.
— In case of 1009, only one branch will be extended as there are no other factors of the number.
Common mistakes and how to avoid them in the factors of 1009
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 1009. 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 1009 examples
Problem 1
Is 7 a factor of 1009?
To check if 7 is a factor, divide 1009 by 7.
1009÷7=144.14 (not a whole number).
Since the result isn’t a whole number, 7 is not a factor of 1009.
Explanation
A factor of 1009 must divide evenly into 1009 without leaving any remainder. Since 7 doesn’t do that, it’s not a factor.
Problem 2
Is 1009 a prime number?
To determine if 1009 is prime, we need to see if any whole numbers other than 1 and 1009 itself divide evenly into it.
Checking divisibility by smaller primes up to √1009≈31.8:
2: 1009 is odd, so not divisible by 2.
3: Sum of digits 1+0+0+9=101 + 0 + 0 + 9 = 101+0+0+9=10 (not divisible by 3).
5: 1009 doesn’t end in 0 or 5, so it’s not divisible by 5.
Checking through other primes (7, 11, 13, 17, etc.) reveals that none divide evenly.
Since no divisors are found, 1009 is a prime number.
Explanation
A prime number has no factors other than 1 and itself. Testing divisibility up to √1009 is enough to confirm this, as factors repeat after the square root.
Problem 3
Which of the following is a factor of 1009: 1, 10, 100, 1009?
The factors of 1009 are 1 and 1009 since it’s a prime number.
Among the options, only 1 and 1009 are factors.
Explanation
Multiples and factors are different. Factors divide into 1009 without a remainder. Here, only 1 and 1009 do that, making them the correct choices.
FAQs on Factors of 1009
1. Is 1009 a twin prime?
2. What is a prime number that follows 1009?
3.What are the prime factors of 99?
4.What is the cube of 1009 ?
5.Is the cube root of 1009 rational?
Important Glossaries for Factors of 1009
- 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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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.
