Factors of 1420
2026-02-28 11:28 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1420, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1420?

The numbers that divide 1420 evenly are known as factors of 1420.

A factor of 1420 is a number that divides the number without remainder.

The factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, and 1420.

Negative factors of 1420: -1, -2, -4, -5, -10, -20, -71, -142, -284, -355, -710, and -1420.

Prime factors of 1420: 2, 5, and 71.

Prime factorization of 1420: 22 × 5 × 71.

The sum of factors of 1420: 1 + 2 + 4 + 5 + 10 + 20 + 71 + 142 + 284 + 355 + 710 + 1420 = 3024

How to Find Factors of 1420?

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 1420. Identifying the numbers which are multiplied to get the number 1420 is the multiplication method.

Step 1: Multiply 1420 by 1, 1420 × 1 = 1420.

Step 2: Check for other numbers that give 1420 after multiplying

2 × 710 = 1420

4 × 355 = 1420

5 × 284 = 1420

10 × 142 = 1420

20 × 71 = 1420

Therefore, the positive factor pairs of 1420 are: (1, 1420), (2, 710), (4, 355), (5, 284), (10, 142), (20, 71).

All these factor pairs result in 1420.

For every positive factor, there is a negative factor.

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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 1420 by 1, 1420 ÷ 1 = 1420.

Step 2: Continue dividing 1420 by the numbers until the remainder becomes 0.

1420 ÷ 1 = 1420

1420 ÷ 2 = 710

1420 ÷ 4 = 355

1420 ÷ 5 = 284

1420 ÷ 10 = 142

1420 ÷ 20 = 71

Therefore, the factors of 1420 are: 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420.

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: In this process, prime factors of 1420 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1420 ÷ 2 = 710

710 ÷ 2 = 355

355 ÷ 5 = 71

71 ÷ 71 = 1

The prime factors of 1420 are 2, 5, and 71. The prime factorization of 1420 is: 22 × 5 × 71.

Factor Tree

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

Step 1: Firstly, 1420 is divided by 2 to get 710.

Step 2: Now divide 710 by 2 to get 355.

Step 3: Then divide 355 by 5 to get 71. Here, 71 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 1420 is: 22 × 5 × 71.

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 1420: (1, 1420), (2, 710), (4, 355), (5, 284), (10, 142), and (20, 71).

Negative factor pairs of 1420: (-1, -1420), (-2, -710), (-4, -355), (-5, -284), (-10, -142), and (-20, -71).

Common Mistakes and How to Avoid Them in Factors of 1420

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 10 people and 1420 marbles. How will they divide it equally?

Okay, lets begin

They will get 142 marbles each.

Explanation

To divide the marbles equally, we need to divide the total marbles with the number of people.

1420/10 = 142

Well explained 👍

Problem 2

A wall is 20 meters long and has a total area of 1420 square meters. Find the height of the wall.

Okay, lets begin

71 meters.

Explanation

To find the height of the wall, we use the formula,

Area = length × height

1420 = 20 × height

To find the value of height, we need to shift 20 to the left side.

1420/20 = height

Height = 71.

Well explained 👍

Problem 3

There are 142 bags and 1420 candies. How many candies will be in each bag?

Okay, lets begin

Each bag will have 10 candies.

Explanation

To find the candies in each bag, divide the total candies with the bags.

1420/142 = 10

Well explained 👍

Problem 4

In a class, there are 355 students, and 5 groups. How many students are there in each group?

Okay, lets begin

There are 71 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

355/5 = 71

Well explained 👍

Problem 5

1420 books need to be arranged in 71 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 20 books.

Explanation

Divide total books with shelves.

1420/71 = 20

Well explained 👍

FAQs on Factors of 1420

1.What are the factors of 1420?

1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 are the factors of 1420.

2.Mention the prime factors of 1420.

The prime factors of 1420 are 22 × 5 × 71.

3.Is 1420 a multiple of 4?

4.Mention the factor pairs of 1420?

(1, 1420), (2, 710), (4, 355), (5, 284), (10, 142), and (20, 71) are the factor pairs of 1420.

5.What is the square of 1420?

The square of 1420 is 2,016,400.

Important Glossaries for Factor of 1420

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, and 1420.
  • Prime factors: The factors which are prime numbers. For example, 2, 5, and 71 are prime factors of 1420.
  • 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 1420 are (1, 1420), (2, 710), etc.
  • Prime factorization: Expressing a number as the product of its prime factors. For instance, the prime factorization of 1420 is 22 × 5 × 71.
  • Multiple: A number that can be divided by another number without a remainder. For example, 1420 is a multiple of 4.

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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.