Factors of 1007
2026-02-28 13:23 Diff

242 Learners

Last updated on December 12, 2025

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 1007, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1007?

The numbers that divide 1007 evenly are known as factors of 1007.

A factor of 1007 is a number that divides the number without a remainder.

The factors of 1007 are 1, 19, 53, and 1007.

Negative factors of 1007: -1, -19, -53, and -1007.

Prime factors of 1007: 19 and 53.

Prime factorization of 1007: 19 × 53.

The sum of factors of 1007: 1 + 19 + 53 + 1007 = 1080

How to Find Factors of 1007?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1007. Identifying the numbers which are multiplied to get the number 1007 is the multiplication method.

Step 1: Multiply 1007 by 1, 1007 × 1 = 1007.

Step 2: Check for other numbers that give 1007 after multiplying 19 × 53 = 1007

Therefore, the positive factor pairs of 1007 are: (1, 1007) and (19, 53).

All these factor pairs result in 1007.

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with 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 1007 by 1, 1007 ÷ 1 = 1007.

Step 2: Continue dividing 1007 by the numbers until the remainder becomes 0.

1007 ÷ 1 = 1007

1007 ÷ 19 = 53

Therefore, the factors of 1007 are: 1, 19, 53, 1007.

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: In this process, prime factors of 1007 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1007 ÷ 19 = 53

53 ÷ 53 = 1

The prime factors of 1007 are 19 and 53.

The prime factorization of 1007 is: 19 × 53.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

Step 1: Firstly, 1007 is divided by 19 to get 53.

Step 2: Now divide 53 by 53 to get 1. Here, 53 is the smallest prime number and cannot be divided anymore. So, the prime factorization of 1007 is: 19 × 53.

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 1007: (1, 1007) and (19, 53).

Negative factor pairs of 1007: (-1, -1007) and (-19, -53).

Common Mistakes and How to Avoid Them in Factors of 1007

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 19 teams and 1007 fans. How will they distribute the fans equally among the teams?

Okay, lets begin

They will have 53 fans each.

Explanation

To distribute the fans equally, we need to divide the total fans by the number of teams.

1007/19 = 53

Well explained 👍

Problem 2

A rectangular painting has a length of 53 cm and a total area of 1007 square cm. Find the width.

Okay, lets begin

19 cm.

Explanation

To find the width of the painting, we use the formula,

Area = length × width

1007 = 53 × width

To find the value of width, we need to shift 53 to the left side.

1007/53 = width

Width = 19.

Well explained 👍

Problem 3

There are 53 boxes and 1007 candies. How many candies will be in each box?

Okay, lets begin

Each box will have 19 candies.

Explanation

To find the candies in each box, divide the total candies by the boxes.

1007/53 = 19

Well explained 👍

Problem 4

In a competition, there are 1007 participants, and 19 groups. How many participants are there in each group?

Okay, lets begin

There are 53 participants in each group.

Explanation

Dividing the participants by the total groups, we will get the number of participants in each group.

1007/19 = 53

Well explained 👍

Problem 5

1007 books need to be arranged in 19 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 53 books.

Explanation

Divide total books by shelves.

1007/19 = 53

Well explained 👍

FAQs on Factors of 1007

1.What are the factors of 1007?

1, 19, 53, 1007 are the factors of 1007.

2.Mention the prime factors of 1007.

The prime factors of 1007 are 19 × 53.

3.Is 1007 a multiple of 19?

4.Mention the factor pairs of 1007.

(1, 1007) and (19, 53) are the factor pairs of 1007.

5.What is the square of 1007?

The square of 1007 is 1,014,049.

Important Glossaries for Factor of 1007

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1007 are 1, 19, 53, and 1007.
     
  • Prime factors: The factors which are prime numbers. For example, 19 and 53 are prime factors of 1007.
     
  • 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 1007 are (1, 1007) and (19, 53).
     
  • Prime factorization: The process of breaking down a composite number into its prime factors. For example, the prime factorization of 1007 is 19 × 53.
     
  • Negative factors: The negative counterparts of the positive factors of a number. For example, the negative factors of 1007 are -1, -19, -53, and -1007.

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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.