100 LearnersLast updated on May 26th, 2025
Factors of 1472
Factors are the numbers that divide any given number evenly without a 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 1472, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1472?
The numbers that divide 1472 evenly are known as factors of 1472.
A factor of 1472 is a number that divides the number without a remainder.
The factors of 1472 are 1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 184, 368, 736, and 1472.
Negative factors of 1472: -1, -2, -4, -8, -16, -23, -32, -46, -64, -92, -184, -368, -736, and -1472.
Prime factors of 1472: 2 and 23.
Prime factorization of 1472: 2^5 × 23.
The sum of factors of 1472: 1 + 2 + 4 + 8 + 16 + 23 + 32 + 46 + 64 + 92 + 184 + 368 + 736 + 1472 = 3048
How to Find Factors of 1472?
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 1472. Identifying the numbers which are multiplied to get the number 1472 is the multiplication method.
Step 1: Multiply 1472 by 1, 1472 × 1 = 1472.
Step 2: Check for other numbers that give 1472 after multiplying:
2 × 736 = 1472
4 × 368 = 1472
8 × 184 = 1472
16 × 92 = 1472
23 × 64 = 1472
32 × 46 = 1472
Therefore, the positive factor pairs of 1472 are: (1, 1472), (2, 736), (4, 368), (8, 184), (16, 92), (23, 64), and (32, 46).
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 1472 by 1, 1472 ÷ 1 = 1472.
Step 2: Continue dividing 1472 by the numbers until the remainder becomes 0.
1472 ÷ 1 = 1472
1472 ÷ 2 = 736
1472 ÷ 4 = 368
1472 ÷ 8 = 184
1472 ÷ 16 = 92
1472 ÷ 23 = 64
1472 ÷ 32 = 46
Therefore, the factors of 1472 are: 1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 184, 368, 736, and 1472.
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 1472 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1472 ÷ 2 = 736
736 ÷ 2 = 368
368 ÷ 2 = 184
184 ÷ 2 = 92
92 ÷ 2 = 46
46 ÷ 2 = 23
23 ÷ 23 = 1
The prime factors of 1472 are 2 and 23.
The prime factorization of 1472 is: 2^5 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1472 is divided by 2 to get 736.
Step 2: Now divide 736 by 2 to get 368.
Step 3: Then divide 368 by 2 to get 184.
Step 4: Divide 184 by 2 to get 92.
Step 5: Divide 92 by 2 to get 46.
Step 6: Divide 46 by 2 to get 23.
Here, 23 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1472 is: 2^5 × 23.
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 1472: (1, 1472), (2, 736), (4, 368), (8, 184), (16, 92), (23, 64), and (32, 46).
Negative factor pairs of 1472: (-1, -1472), (-2, -736), (-4, -368), (-8, -184), (-16, -92), (-23, -64), and (-32, -46).
Common Mistakes and How to Avoid Them in Factors of 1472
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 1472, 1 and 1472 are also factors.
Factors of 1472 Examples
Problem 1
There are 736 apples and 2 baskets. How will they divide it equally?
They will get 368 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
736/2 = 368
Problem 2
A field is rectangular, the length of the field is 92 meters and the total area is 1472 square meters. Find the width?
16 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1472 = 92 × width
To find the value of width, we need to shift 92 to the left side.
1472/92 = width
Width = 16.
Problem 3
There are 23 boxes and 1472 candies. How many candies will be in each box?
Each box will have 64 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
1472/23 = 64
Problem 4
In a class, there are 368 students, and 8 groups. How many students are there in each group?
There are 46 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
368/8 = 46
Problem 5
1472 books need to be arranged in 46 shelves. How many books will go on each shelf?
Each of the shelves has 32 books.
Explanation
Divide total books by shelves.
1472/46 = 32
FAQs on Factors of 1472
1.What are the factors of 1472?
2.Mention the prime factors of 1472.
3.Is 1472 a multiple of 16?
4.Mention the factor pairs of 1472?
5.What is the square of 1472?
Important Glossaries for Factor of 1472
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1472 are 1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 184, 368, 736, and 1472.
- Prime factors: The factors which are prime numbers. For example, 2 and 23 are prime factors of 1472.
- 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 1472 are (1, 1472), (2, 736), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1472 is 2^5 × 23.
- Negative factors: Factors of a number that are negative. For example, the negative factors of 1472 include -1, -2, -4, etc.
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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.
