109 LearnersLast updated on June 10th, 2025
Factors of 1504
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 1504, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1504?
The numbers that divide 1504 evenly are known as factors of 1504.
A factor of 1504 is a number that divides the number without remainder.
The factors of 1504 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752, and 1504.
Negative factors of 1504: -1, -2, -4, -8, -16, -47, -94, -188, -376, -752, and -1504.
Prime factors of 1504: 2 and 47.
Prime factorization of 1504: 24 × 47.
The sum of factors of 1504: 1 + 2 + 4 + 8 + 16 + 47 + 94 + 188 + 376 + 752 + 1504 = 2992
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How to Find Factors of 1504?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1504. Identifying the numbers which are multiplied to get the number 1504 is the multiplication method.
Step 1: Multiply 1504 by 1, 1504 × 1 = 1504.
Step 2: Check for other numbers that give 1504 after multiplying
2 × 752 = 1504
4 × 376 = 1504
8 × 188 = 1504
16 × 94 = 1504
47 × 32 = 1504
Therefore, the positive factor pairs of 1504 are: (1, 1504), (2, 752), (4, 376), (8, 188), (16, 94), and (47, 32).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1504 by 1, 1504 ÷ 1 = 1504.
Step 2: Continue dividing 1504 by the numbers until the remainder becomes 0.
1504 ÷ 1 = 1504
1504 ÷ 2 = 752
1504 ÷ 4 = 376
1504 ÷ 8 = 188
1504 ÷ 16 = 94
1504 ÷ 47 = 32
Therefore, the factors of 1504 are: 1, 2, 4, 8, 16, 47, 94, 188, 376, 752, 1504.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 1504 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1504 ÷ 2 = 752
752 ÷ 2 = 376
376 ÷ 2 = 188
188 ÷ 2 = 94
94 ÷ 2 = 47
47 ÷ 47 = 1
The prime factors of 1504 are 2 and 47.
The prime factorization of 1504 is: 24 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1504 is divided by 2 to get 752.
Step 2: Now divide 752 by 2 to get 376.
Step 3: Then divide 376 by 2 to get 188.
Step 4: Divide 188 by 2 to get 94.
Step 5: Divide 94 by 2 to get 47. Here, 47 is the smallest prime number that cannot be divided further. So, the prime factorization of 1504 is: 24 × 47.
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 1504: (1, 1504), (2, 752), (4, 376), (8, 188), (16, 94), and (47, 32).
Negative factor pairs of 1504: (-1, -1504), (-2, -752), (-4, -376), (-8, -188), (-16, -94), and (-47, -32).
Common Mistakes and How to Avoid Them in Factors of 1504
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 1504, 1 and 1504 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 1504 consist of -1, -2, -4, 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 1504/1.5 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 1504 are prime numbers.
For example, 2 and 47 are the prime factors of 1504, but it has other factors like 4, 16.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1504 as 24 × 47 and missing all the key factors.
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Factors of 1504 Examples
Problem 1
A garden has 16 rows and 1504 plants. How many plants are there in each row?
There are 94 plants in each row.
Explanation
To find the number of plants in each row, we need to divide the total plants by the number of rows.
1504/16 = 94
Problem 2
A construction project has a rectangular area of 1504 square meters and a width of 32 meters. What is the length of the area?
47 meters.
Explanation
To find the length of the area, we use the formula, Area = length × width
1504 = 32 × length
To find the value of length, we need to divide 1504 by 32.
1504/32 = length
Length = 47.
Problem 3
There are 188 boxes and 1504 items. How many items will be in each box?
Each box will have 8 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
1504/188 = 8
Problem 4
A library has 752 books, and each shelf holds 2 shelves. How many books are there on each shelf?
There are 376 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
752/2 = 376
Problem 5
There are 47 teams in a tournament and each team plays 32 matches. What is the total number of matches played in the tournament?
The total number of matches played is 1504.
Explanation
Multiply the number of teams by the number of matches each team plays.
47 × 32 = 1504
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FAQs on Factors of 1504
1.What are the factors of 1504?
2.Mention the prime factors of 1504.
3.Is 1504 a multiple of 4?
4.Mention the factor pairs of 1504?
5.What is the square of 1504?
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Important Glossaries for Factor of 1504
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1504 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752, and 1504.
- Prime factors: The factors which are prime numbers. For example, 2 and 47 are prime factors of 1504.
- 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 1504 are (1, 1504), (2, 752), etc.
- Prime Factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1504 is 24 × 47.
- Negative Factors: Factors that are negative integers. For example, the negative factors of 1504 are -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.
