125 LearnersLast updated on May 26th, 2025
Factors of 420
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 420, how they are used in real life, and tips to learn them quickly.
What are the Factors of 420?
The numbers that divide 420 evenly are known as factors of 420.
A factor of 420 is a number that divides the number without a remainder.
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420.
Negative factors of 420: -1, -2, -3, -4, -5, -6, -7, -10, -12, -14, -15, -20, -21, -28, -30, -35, -42, -60, -70, -84, -105, -140, -210, and -420.
Prime factors of 420: 2, 3, 5, and 7.
Prime factorization of 420: 2^2 × 3 × 5 × 7.
The sum of factors of 420: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 28 + 30 + 35 + 42 + 60 + 70 + 84 + 105 + 140 + 210 + 420 = 1206
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How to Find Factors of 420?
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 420. Identifying the numbers which are multiplied to get the number 420 is the multiplication method.
Step 1: Multiply 420 by 1, 420 × 1 = 420.
Step 2: Check for other numbers that give 420 after multiplying
2 × 210 = 420
3 × 140 = 420
4 × 105 = 420
5 × 84 = 420
6 × 70 = 420
7 × 60 = 420
10 × 42 = 420
12 × 35 = 420
14 × 30 = 420
15 × 28 = 420
20 × 21 = 420
Therefore, the positive factor pairs of 420 are: (1, 420), (2, 210), (3, 140), (4, 105), (5, 84), (6, 70), (7, 60), (10, 42), (12, 35), (14, 30), (15, 28), (20, 21).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 the simple division method -
Step 1: Divide 420 by 1, 420 ÷ 1 = 420.
Step 2: Continue dividing 420 by the numbers until the remainder becomes 0.
420 ÷ 1 = 420
420 ÷ 2 = 210
420 ÷ 3 = 140
420 ÷ 4 = 105
420 ÷ 5 = 84
420 ÷ 6 = 70
420 ÷ 7 = 60
420 ÷ 10 = 42
420 ÷ 12 = 35
420 ÷ 14 = 30
420 ÷ 15 = 28
420 ÷ 20 = 21
Therefore, the factors of 420 are: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420.
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 420 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
420 ÷ 2 = 210 210 ÷ 2 = 105 105 ÷ 3 = 35 35 ÷ 5 = 7 7 ÷ 7 = 1
The prime factors of 420 are 2, 3, 5, and 7.
The prime factorization of 420 is: 2^2 × 3 × 5 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 420 is divided by 2 to get 210.
Step 2: Now divide 210 by 2 to get 105.
Step 3: Then divide 105 by 3 to get 35.
Step 4: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 420 is: 2^2 × 3 × 5 × 7.
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 420: (1, 420), (2, 210), (3, 140), (4, 105), (5, 84), (6, 70), (7, 60), (10, 42), (12, 35), (14, 30), (15, 28), (20, 21).
Negative factor pairs of 420: (-1, -420), (-2, -210), (-3, -140), (-4, -105), (-5, -84), (-6, -70), (-7, -60), (-10, -42), (-12, -35), (-14, -30), (-15, -28), (-20, -21).
Common Mistakes and How to Avoid Them in Factors of 420
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 420, 1 and 420 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors. Always check whether you have mentioned negative factors.
For example, the factors of 420 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes incorrectly add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 420/1.5 = 280, and it 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 420 are prime numbers.
For example, 2, 3, 5, and 7 are the prime factors of 420, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 420 as 2^2 × 3 × 5 × 7 and missing all the key factors.
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Factors of 420 Examples
Problem 1
There are 21 teams and 420 fans. How will they distribute the fans equally?
They will have 20 fans each.
Explanation
To distribute the fans equally, divide the total fans by the number of teams.
420/21 = 20
Problem 2
A rectangular plot has a length of 30 meters and a total area of 420 square meters. Find the width.
14 meters.
Explanation
To find the width of the plot, use the formula, Area = length × width 420 = 30 × width
To find the value of width, move 30 to the left side.
420/30 = width
Width = 14.
Problem 3
There are 35 boxes and 420 apples. How many apples will be in each box?
Each box will have 12 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
420/35 = 12
Problem 4
In a competition, there are 60 participants and 7 groups. How many participants are there in each group?
There are 9 participants in each group.
Explanation
Dividing the participants by the total groups will give the number of participants in each group.
60/7 = 8.57 (rounded to 9 for practical distribution)
Problem 5
A library needs to organize 420 books into 12 categories. How many books will go in each category?
Each category will have 35 books.
Explanation
Divide total books by categories.
420/12 = 35
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FAQs on Factors of 420
1.What are the factors of 420?
2.Mention the prime factors of 420.
3.Is 420 a multiple of 6?
4.Mention the factor pairs of 420?
5.What is the square of 420?
6.How can children in Canada use numbers in everyday life to understand Factors of 420?
7.What are some fun ways kids in Canada can practice Factors of 420 with numbers?
8.What role do numbers and Factors of 420 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 420 skills?
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Important Glossaries for Factor of 420
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 420.
- 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 420 are (1, 420), (2, 210), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For 420, it's 2^2 × 3 × 5 × 7.
- Multiple: A multiple of a number is the product of that number with an integer. For example, 420 is a multiple of 6.
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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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