# Factors of 420

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

#### How to find factors of a number

 1.   Find factors of 420 using Division Method 2.   Find factors of 420 using Prime Factorization 3.   Find factors of 420 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 420

• Divide 420 by 1: 420 ÷ 1 : Remainder = 0
• Divide 420 by 2: 420 ÷ 2 : Remainder = 0
• Divide 420 by 3: 420 ÷ 3 : Remainder = 0
• Divide 420 by 4: 420 ÷ 4 : Remainder = 0
• Divide 420 by 5: 420 ÷ 5 : Remainder = 0
• Divide 420 by 6: 420 ÷ 6 : Remainder = 0
• Divide 420 by 7: 420 ÷ 7 : Remainder = 0
• Divide 420 by 10: 420 ÷ 10 : Remainder = 0
• Divide 420 by 12: 420 ÷ 12 : Remainder = 0
• Divide 420 by 14: 420 ÷ 14 : Remainder = 0
• Divide 420 by 15: 420 ÷ 15 : Remainder = 0
• Divide 420 by 20: 420 ÷ 20 : Remainder = 0
• Divide 420 by 21: 420 ÷ 21 : Remainder = 0
• Divide 420 by 28: 420 ÷ 28 : Remainder = 0
• Divide 420 by 30: 420 ÷ 30 : Remainder = 0
• Divide 420 by 35: 420 ÷ 35 : Remainder = 0
• Divide 420 by 42: 420 ÷ 42 : Remainder = 0
• Divide 420 by 60: 420 ÷ 60 : Remainder = 0
• Divide 420 by 70: 420 ÷ 70 : Remainder = 0
• Divide 420 by 84: 420 ÷ 84 : Remainder = 0
• Divide 420 by 105: 420 ÷ 105 : Remainder = 0
• Divide 420 by 140: 420 ÷ 140 : Remainder = 0
• Divide 420 by 210: 420 ÷ 210 : Remainder = 0
• Divide 420 by 420: 420 ÷ 420 : Remainder = 0

Hence, 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

#### 2. Steps to find factors of 420 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 420 using the division method, follow these steps:

• Step 1. Start dividing 420 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 420, which is 2. Divide 420 by 2 to obtain the quotient (210).
420 ÷ 2 = 210
• Step 3. Repeat step 1 with the obtained quotient (210).
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 420 is, 420 = 2 x 2 x 3 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 420 as shown below:

So, the prime factorization of 420 is, 420 = 2 x 2 x 3 x 5 x 7.

#### 3. Find factors of 420 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 420 would be the two numbers which, when multiplied, give 420 as the result.

The following table represents the calculation of factors of 420 in pairs:

Factor Pair Pair Factorization
1 and 420 1 x 420 = 420
2 and 210 2 x 210 = 420
3 and 140 3 x 140 = 420
4 and 105 4 x 105 = 420
5 and 84 5 x 84 = 420
6 and 70 6 x 70 = 420
7 and 60 7 x 60 = 420
10 and 42 10 x 42 = 420
12 and 35 12 x 35 = 420
14 and 30 14 x 30 = 420
15 and 28 15 x 28 = 420
20 and 21 20 x 21 = 420

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 420. They are called negative pair factors.

Hence, the negative pairs of 420 would be ( -1 , -420 ) , ( -2 , -210 ) , ( -3 , -140 ) , ( -4 , -105 ) , ( -5 , -84 ) , ( -6 , -70 ) , ( -7 , -60 ) , ( -10 , -42 ) , ( -12 , -35 ) , ( -14 , -30 ) , ( -15 , -28 ) and ( -20 , -21 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 420 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 420.
• Every number is a factor of zero (0), since 420 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are exact divisors of 420.
• 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. Each factor divides 420 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are all less than or equal to 420.

• How do you find factors of a negative number? ( eg. -420 )?

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.

• What is the sum of all factors of 420?

The sum of all factors of 420 is 1344.

• What is prime factorization of 420?

Prime factorization of 420 is 2 x 2 x 3 x 5 x 7.

• What are the pair factors of 420?

Pair factors 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).

• What are six multiples of 420?

First five multiples of 420 are 840, 1260, 1680, 2100, 2520, 2940.

• Is 420 a whole number?

Yes 420 is a whole number.

• Which is the smallest prime factor of 420?

Smallest prime factor of 420 is 2.

• What are five multiples of 420?

First five multiples of 420 are 840, 1260, 1680, 2100, 2520.

• Write all factors of 420?

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.

#### Examples of Factors

Joey wants to write all the prime factors of 420 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 420 are 2, 2, 3, 5, 7.
So in exponential form it can be written as 22 x 3 x 5 x 7.

How many factors are there for 420?

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.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 420. Can you predict the answer?

23 factor(s) 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.

Sammy is puzzled while calculating the prime factors of 420. Can you help him find them?

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 of 420 are 2, 2, 3, 5, 7

What is prime factorization of 420?

Prime factorization of 420 is 2 x 2 x 3 x 5 x 7 = 22 x 3 x 5 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 420. Can you help her?

Prime factors of 420 are 2, 2, 3, 5, 7.
Hence, the product of prime factors of 210.

Can you help Rubel to find out the product of the even factors of 420?

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.
Even factors of 420 are 2, 4, 6, 10, 12, 14, 20, 28, 30, 42, 60, 70, 84, 140, 210, 420.
Hence, product of even factors of 420 is; 2 x 4 x 6 x 10 x 12 x 14 x 20 x 28 x 30 x 42 x 60 x 70 x 84 x 140 x 210 x 420 = 2.478758911082496e+23.