130 LearnersLast updated on May 26th, 2025
Factors of 1428
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1428, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1428?
The numbers that divide 1428 evenly are known as factors of 1428.
A factor of 1428 is a number that divides the number without remainder.
The factors of 1428 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 284, 428, 476, 714, and 1428.
Negative factors of 1428: -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -284, -428, -476, -714, and -1428.
Prime factors of 1428: 2, 3, and 17.
Prime factorization of 1428: 2² × 3² × 17.
The sum of factors of 1428: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 17 + 18 + 34 + 36 + 51 + 68 + 102 + 153 + 204 + 284 + 428 + 476 + 714 + 1428 = 4044
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How to Find Factors of 1428?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1428. Identifying the numbers which are multiplied to get the number 1428 is the multiplication method.
Step 1: Multiply 1428 by 1, 1428 × 1 = 1428.
Step 2: Check for other numbers that give 1428 after multiplying
2 × 714 = 1428
3 × 476 = 1428
4 × 357 = 1428
6 × 238 = 1428
9 × 158 = 1428
12 × 119 = 1428
17 × 84 = 1428
18 × 79 = 1428
Therefore, the positive factor pairs of 1428 are: (1, 1428), (2, 714), (3, 476), (4, 357), (6, 238), (9, 158), (12, 119), (17, 84), (18, 79).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 1428 by 1, 1428 ÷ 1 = 1428.
Step 2: Continue dividing 1428 by the numbers until the remainder becomes 0.
1428 ÷ 1 = 1428
1428 ÷ 2 = 714
1428 ÷ 3 = 476
1428 ÷ 4 = 357
1428 ÷ 6 = 238
1428 ÷ 9 = 158
1428 ÷ 12 = 119
1428 ÷ 17 = 84
1428 ÷ 18 = 79
Therefore, the factors of 1428 are: 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 284, 428, 476, 714, 1428.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1428 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1428 ÷ 2 = 714
714 ÷ 2 = 357
357 ÷ 3 = 119
119 ÷ 17 = 7
7 ÷ 7 = 1
The prime factors of 1428 are 2, 3, and 17.
The prime factorization of 1428 is: 2² × 3 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1428 is divided by 2 to get 714.
Step 2: Now divide 714 by 2 to get 357.
Step 3: Then divide 357 by 3 to get 119.
Step 4: Divide 119 by 17 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1428 is: 2² × 3 × 17.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1428: (1, 1428), (2, 714), (3, 476), (4, 357), (6, 238), (9, 158), (12, 119), (17, 84), (18, 79).
Negative factor pairs of 1428: (-1, -1428), (-2, -714), (-3, -476), (-4, -357), (-6, -238), (-9, -158), (-12, -119), (-17, -84), (-18, -79).
Common Mistakes and How to Avoid Them in Factors of 1428
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1428, 1 and 1428 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1428 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1428/1.5 = 952, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 1428 are prime numbers.
For example, 2, 3, and 17 are the prime factors of 1428, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1428 as 2² × 3 × 17 and missing all the key factors.
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Factors of 1428 Examples
Problem 1
There are 714 apples and 2 baskets. How will they divide it equally?
They will get 357 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of baskets.
714/2 = 357
Problem 2
A garden is rectangular, the length of the garden is 18 meters, and the total area is 1428 square meters. Find the width?
79 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1428 = 18 × width
To find the value of width, we need to shift 18 to the left side.
1428/18 = width
Width = 79.
Problem 3
There are 12 boxes and 1428 marbles. How many marbles will be in each box?
Each box will have 119 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
1428/12 = 119
Problem 4
In a seminar, there are 1428 participants, and 9 groups. How many participants are there in each group?
There are 158 participants in each group.
Explanation
Dividing the participants with the total groups, we will get the number of participants in each group.
1428/9 = 158
Problem 5
1428 pages need to be bound into 6 books. How many pages will go in each book?
Each book will have 238 pages.
Explanation
Divide total pages with books.
1428/6 = 238
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FAQs on Factors of 1428
1.What are the factors of 1428?
2.Mention the prime factors of 1428.
3.Is 1428 a multiple of 4?
4.Mention the factor pairs of 1428?
5.What is the square of 1428?
6.How can children in Canada use numbers in everyday life to understand Factors of 1428?
7.What are some fun ways kids in Canada can practice Factors of 1428 with numbers?
8.What role do numbers and Factors of 1428 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1428 skills?
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Important Glossaries for Factors of 1428
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1428 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 284, 428, 476, 714, and 1428.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 1428.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1428 are (1, 1428), (2, 714), etc.
- Prime factorization: The representation of a number as the product of its prime factors. For example, the prime factorization of 1428 is 2² × 3 × 17.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the given number. For example, using this method, we find that 2 × 714 = 1428.
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Hiralee Lalitkumar Makwana
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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.
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