173 LearnersLast updated on May 26th, 2025
Factors of 228
What's your say about the factors of 228? Factors are essentially numbers that can be multiplied together to give an original number. In other words, finding those perfect pairs that go into making 228 without leaving a remainder.
What are the factors of 228?
Similarly, as we learned above, factors of 228 are such numbers that will be multiplied to get 228. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.
228 has only twelve factors: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228.
Negative factors of 228
Negative factors are nothing but the negative counterparts of the position factors of a number.
Since 228 has twelve positive factors: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228, it will also have twelve negative counterparts: -1, -2, -3, -4, -6, -12, -19, -38, -57, -76, -114, and -228.
Prime factors of 228: Since 228 is a composite number, it has 2, 3, and 19 as its prime factor.
Prime factorization of 228: Prime factorization of a number is the method of expressing 228 as a product of prime factors.
The prime factorization of 228 = 22 × 31× 191
How to find the factors of 228
There are several ways of finding factors of 228. We will learn about them one by one as we go on.
Finding factors using multiplication
In this method, we will try to find such a pair of numbers that will give 228 as their product. We recommend that you should follow the following steps to find factors using multiplication.
Step 1: Always look for a pair of numbers whose product is 228.
Step 2: After finding such pairs, list them all one by one.
Here, factor pairs of 228 are (1, 228), (2, 144), (3, 76), (4, 57), (6, 38), (8, 36), (12, 19).
So the factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228.
Finding factors by division method
In the method, we need to find such numbers that divide 228 completely without leaving any remainder.
228/1 = 228
228/ 2 = 89
228/ 3 = 76
228/ 4 = 57
228/ 6 = 38
228/ 12 = 19
228/ 19 = 12
228/ 38 = 6
228/ 57 = 4
228/ 76 = 3
228/ 114 = 2
228/ 228 = 1
All the 12 numbers: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228, mentioned above divide 228 completely without any remainder. Hence, they are factors of 228.
Prime Factors and Prime Factorization
In the prime factorization method, a number is expressed as the product of prime factors.
Here, as we know, 228 = 22 × 31 × 191
2, 3, and 19 are the prime factors when multiplied together will give 228 as a product of the multiplication.
Factor tree
A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.
The factor pairs of 228 are (1, 228), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)
Positive Pair Factors of 228 are (1, 228), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)
Negative Pair Factors of 228 are (-1, -228), (-2, -245), (-5, -98), (-7, -70), (-10, -49), and (-14, -35)
Common Mistakes and How to Avoid Them in Factors Of 228
There are some errors that a child is bound to commit while discovering the factors of 228. Let us know what error a child is likely to commit.
Mistake 1
A child might consider only the prime factors and leave other factors.
A child must know that a number has both prime and composite factors.
Factors of 228 examples
Problem 1
What is a quarter of 228?
57 is the quarter of 228
Explanation
a quarter of 228 means one-fourth of 228, which is 57.
Problem 2
Fill in the blanks for prime factorization of 228= _ * _ * _ * 19
2 × 2 × 3 would be filled in the blanks respectively.
Explanation
We know that 2× 2× 3×19 = 228. So, 2, 2, and 3 are to be filled in the blanks respectively.
Problem 3
Determine the sum of the largest and smallest prime factor of 228.
21 is the sum of the largest and smallest prime factor of 228.
Explanation
228 = 2 × 2 × 3 × 19. The largest and the smallest prime factors are 2 and 19 respectively. So, 19 + 2 = 21.
Problem 4
Calculate the average sum of all the factors of 228.
The average sum of all factors of 228 is 46.67.
Explanation
The sum of all the factors of 228 is 560. The average sum is equal to 560/12= 46.67.
Problem 5
Find the factor pairs of 228 whose sum of the factors are 116 and 61.
The factor pairs are (2, 114) and (4, 57).
Explanation
Perform the sum of 2 + 114 and 4 + 57, 116 and 61 respectively.
FAQs on factors of 228
1.Can you divide infinity into half?
2. Why is zero a rational number?
3.Can you determine if negative numbers can be divided into odd and even numbers?
4.Can you mention the first odd positive number?
5. Are there any negative prime numbers?
Important Glossaries for Factors of 228
- Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.
- Composite Numbers: Those numbers that have more than 2 factors.
- Negative Factors: These are the counterparts of the positive factors of a number.
- Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.
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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.
