195 LearnersLast updated on May 26th, 2025
Factors of 330
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 330 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 330?
Factors are whole numbers that, when multiplied, the product is equal to 330.
330 is not a prime number, its factors are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165 and 330. For every factor, there is a corresponding negative factor, for 330, the negative factors -1, -2, -3, -5, -6, -10, -11, -15, -22, -30, -33, -55, -66, -110, -165 and -330.
How to find the factors of 330?
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 330.
Step 2: All the pairs found represent the factors of 330.
330 is not a prime number. The pair of numbers whose product is 330 is;
1×330=330
2×165 = 330
3×110 = 330
5×66=330
6×55=330
10×33=330
11×30=330
15×22=330
The factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165 and 330.
Finding Factors by Division Method
Step 1: Start by dividing 330 with the smallest number, and check the remainders.
Step 2: 330 is not prime, therefore the divisors it has are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165 and 330. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165 and 330.
Prime factors and prime factorization
— 330 is not a prime number.
— The prime factorization of 330 is 2×3×5×11.
— Factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165 and 330.
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 330, branch will be extended as the number is prime factorized as 2×165 → 3×55 → 5×11. 11 is a prime number and cannot be factored further.
Common mistakes and how to avoid them in factors of 330
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 330. 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 330 Examples
Problem 1
How many factors does 330 have?
First, find the prime factorization of 330:
330=2×3×5×11.
Using the formula for finding the total number of factors, add 1 to each of the exponents and multiply:
(1+1)×(1+1)×(1+1)×(1+1)=2×2×2×2=16
So, 330 has 16 factors.
Explanation
To find the number of factors, we add 1 to each exponent in the prime factorization and multiply the results. This gives the total count of factors for the number 330.
Problem 2
Find the sum of all the factors of 330.
First, use the prime factorization:
330=21×31×51×111
Apply the formula to find the sum of factors by adding one to each power and summing each series:
(20+21)×(30+31)×(50+51)×(110+111)
=(1+2)×(1+3)×(1+5)×(1+11)
=3×4×6×12=864
So, the sum of all factors of 330 is 864.
Explanation
Using the formula for the sum of divisors of a number, we take each prime factor, raise it to each power from 0 up to the exponent, and sum the terms. Then, we multiply these sums to get the total sum of all factors.
Problem 3
What are the common factors of 330 and 198?
Find the factors of 330: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, and 330.
Find the factors of 198: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198.
Identify the common factors: 1, 2, 3, 6, 11, 22, 33, and 66.
The common factors of 330 and 198 are 1, 2, 3, 6, 11, 22, 33, and 66.
Explanation
Common factors are shared divisors between two numbers. We find each number’s factors and then pick the ones that appear in both lists.
FAQs on Factors of 330
1.What is the number name for 330?
2.Is 0 a multiple of 330?
3.What are the factors of 333?
4.Is 330 divisible by 8?
5.Prime factorize 330.
6.How can children in Qatar use numbers in everyday life to understand Factors of 330?
7.What are some fun ways kids in Qatar can practice Factors of 330 with numbers?
8.What role do numbers and Factors of 330 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 330 skills?
Important Glossaries for Factors of 330
- 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 Qatar
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.
