102 LearnersLast updated on May 26th, 2025
Factors of 1456
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 1456, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1456?
The numbers that divide 1456 evenly are known as factors of 1456.
A factor of 1456 is a number that divides the number without remainder.
The factors of 1456 are 1, 2, 4, 8, 13, 16, 26, 29, 52, 58, 104, 116, 208, 232, 377, 464, 754, and 1456.
Negative factors of 1456: -1, -2, -4, -8, -13, -16, -26, -29, -52, -58, -104, -116, -208, -232, -377, -464, -754, and -1456.
Prime factors of 1456: 2, 13, and 29.
Prime factorization of 1456: \(2^4 \times 13 \times 29\).
The sum of factors of 1456: 1 + 2 + 4 + 8 + 13 + 16 + 26 + 29 + 52 + 58 + 104 + 116 + 208 + 232 + 377 + 464 + 754 + 1456 = 3920
How to Find Factors of 1456?
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 1456. Identifying the numbers which are multiplied to get the number 1456 is the multiplication method.
Step 1: Multiply 1456 by 1, 1456 × 1 = 1456.
Step 2: Check for other numbers that give 1456 after multiplying
2 × 728 = 1456
4 × 364 = 1456
8 × 182 = 1456
13 × 112 = 1456
16 × 91 = 1456
26 × 56 = 1456
29 × 50.206 = 1456 (not a valid factor pair)
Therefore, the positive factor pairs of 1456 are: (1, 1456), (2, 728), (4, 364), (8, 182), (13, 112), (16, 91), and (26, 56). All these factor pairs result in 1456.
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 a simple division method -
Step 1: Divide 1456 by 1, 1456 ÷ 1 = 1456.
Step 2: Continue dividing 1456 by the numbers until the remainder becomes 0.
1456 ÷ 1 = 1456
1456 ÷ 2 = 728
1456 ÷ 4 = 364
1456 ÷ 8 = 182
1456 ÷ 13 = 112
1456 ÷ 16 = 91
1456 ÷ 26 = 56
Therefore, the factors of 1456 are: 1, 2, 4, 8, 13, 16, 26, 29, 52, 58, 104, 116, 208, 232, 377, 464, 754, and 1456.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1456 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1456 ÷ 2 = 728
728 ÷ 2 = 364
364 ÷ 2 = 182
182 ÷ 2 = 91
91 ÷ 13 = 7
7 ÷ 7 = 1
The prime factors of 1456 are 2, 13, and 29.
The prime factorization of 1456 is: \(2^4 \times 13 \times 29\).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1456 is divided by 2 to get 728.
Step 2: Now divide 728 by 2 to get 364.
Step 3: Then divide 364 by 2 to get 182.
Step 4: Divide 182 by 2 to get 91.
Step 5: Divide 91 by 13 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1456 is: \(2^4 \times 13 \times 29\).
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 1456: (1, 1456), (2, 728), (4, 364), (8, 182), (13, 112), (16, 91), (26, 56).
Negative factor pairs of 1456: (-1, -1456), (-2, -728), (-4, -364), (-8, -182), (-13, -112), (-16, -91), (-26, -56).
Common Mistakes and How to Avoid Them in Factors of 1456
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 1456, 1 and 1456 are also factors.
Factors of 1456 Examples
Problem 1
A music festival has 1456 tickets and 13 different performances. How many tickets can be allocated to each performance?
Each performance can have 112 tickets.
Explanation
To divide the tickets equally among performances, we need to divide the total tickets by the number of performances.
1456 ÷ 13 = 112
Problem 2
A rectangular garden has a length of 56 meters and a total area of 1456 square meters. Find the width.
The width is 26 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1456 = 56 × width
To find the value of width, we need to shift 56 to the left side.
1456 ÷ 56 = width
Width = 26.
Problem 3
A warehouse has 16 sections and 1456 crates. How many crates will be in each section?
Each section will have 91 crates.
Explanation
To find the crates in each section, divide the total crates by the sections.
1456 ÷ 16 = 91
Problem 4
A conference hall accommodates 1456 people and has 8 entrances. How many people should use each entrance?
182 people should use each entrance.
Explanation
Dividing the total attendees by the number of entrances, we will get the number of people per entrance.
1456 ÷ 8 = 182
Problem 5
There are 1456 pages to be printed by 4 printers. How many pages should each printer print?
Each printer should print 364 pages.
Explanation
Divide total pages by the number of printers.
1456 ÷ 4 = 364
FAQs on Factors of 1456
1.What are the factors of 1456?
2.Mention the prime factors of 1456.
3.Is 1456 a multiple of 13?
4.Mention the factor pairs of 1456.
5.What is the square of 1456?
6.How can children in India use numbers in everyday life to understand Factors of 1456?
7.What are some fun ways kids in India can practice Factors of 1456 with numbers?
8.What role do numbers and Factors of 1456 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1456 skills?
Important Glossaries for Factors of 1456
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1456 are 1, 2, 4, 8, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 13, and 29 are prime factors of 1456.
- 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 1456 are (1, 1456), (2, 728), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 1456 is \(2^4 \times 13 \times 29\).
- Negative factors: Factors that are negative. For example, -1, -2, -4, -8, etc., are negative factors of 1456.
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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.
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