Factors

# Factors of 21 | Prime Factorization of 21 | Factor Tree of 21

Written by Prerit Jain

Updated on: 08 Jun 2023

Contents

### Factors of 21 | Prime Factorization of 21 | Factor Tree of 21

## Factors of 21

Factors of 21 | Factor Pairs of 21 | Prime factors of 21 |

1, 3, 7, 21 | (1,21) (3,7) (7,3) | 3 x 7 |

**Factors of 21**,

**Factor Pairs of 21**,

**Prime factors of 21**

Calculate Factors of

**The Factors are**

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## What are the factors of 21

The factors of a number are the integers that can be evenly divided into that number without any remainder. For instance, the factors of 6 include 1, 2, 3, and 6 because all of these numbers can be evenly divided into 6. To find the factors of 21, we can divide 21 by each integer from 1 to 21 and see which ones result in a whole number. When we do this, **we find that the factors of 21 are 1, 3, 7, and 21. **This is because these numbers can all be evenly divided into 21 without any remainder.

## How to Find Factors of 21

To find the factors of 21, you can use one of the following methods:

- Factors of 21 using Multiplication Method
- Factors of 21 using the Division Method
- Prime Factorization of 21
- Factor tree of 21

## Factors of 21 Using the Multiplication Method

- Write down the number 21.
- Multiply 1 by 21 to find the first factor. Write down the product.
- Continue multiplying different numbers by 21 until you have found all of the factors. Write down each product as you go.

For example,

1 x 21 = 21

3 x 7 = 21

Using this method, we can see that the factors of 21 are 1, 3, 7, and 21. This is because these numbers can all be evenly multiplied by 21 to produce 21 as the result.

## Factors of 21 Using the Division Method

1. Write down the number 21.

2. Divide 21 by each integer between 1 and 21 to find the factors. Write down each quotient as you go.

3. Continue dividing 21 by different numbers until you have found all of the factors.

For example,

21 / 1 = 21

21 / 3 = 7

21 / 7 = 3

21 / 21 = 1

Using this method, we can see that the factors of 21 are 1, 3, 7, and 21. This is because these numbers can all be used to evenly divide 21 without any remainder.

## Prime Factorization of 21

Calculate Prime Factors of

The Prime Factors of 21 =

3 x

7

**The prime factorization of 21 is 3 x 7.**

To find the prime factorization of a number, you need to find the prime numbers that can be multiplied together to give the original number. For example, the prime factorization of 21 is 3 x 7, because 3 and 7 are prime numbers and 21 can be expressed as the product of one 3 and one 7 (3 x 7 = 21).

The prime factorization of a number is written as the product of its prime factors. For example,** **the prime factorization of 21 is written as 3 x 7.

## Factor tree of 21

- A factor tree is a visual representation of the prime factorization of a number. To find the prime factorization of a number, we can start by dividing the number by the smallest prime number that divides it evenly (without a remainder). This process can be repeated until we are left with only prime numbers.
- For example, to find the prime factorization of 21, we can start by dividing 21 by 3, which gives us a quotient of 7 and a remainder of 0. This means that 21 is divisible by 3, so 3 is a factor of 21. We can then divide 7 by 3 to see if it is also divisible by 3. This gives us a quotient of 2 and a remainder of 1, which means that 7 is not divisible by 3.
- Since 7 is not divisible by 3, we can’t find any more factors of 3. This means that the prime factorization of 21 is 3 x 7. We can represent this as a factor tree, like this:

This shows that 21 can be written as the product of 3 and 7. Since 3 and 7 are both prime numbers, the prime factorization of 21 is complete.

I hope this helps! Let me know if you have any other questions.

## Factor Pairs of 21

Calculate Pair Factors of

1 x 21=21

3 x 7=21

7 x 3=21

So Pair Factors of 21 are

(1,21)

(3,7)

(7,3)

A factor pair of a number is a pair of numbers that can be multiplied together to equal that number. For example, the factor pairs of 21 are (1, 21), (3, 7), and (-1, -21). These are all the pairs of numbers that can be multiplied together to get 21.

We can also say that 1 and 21 are the divisors of 21 since they divide into 21 evenly (without a remainder). All of the factor pairs of 21 are also divisors of 21.

To find the prime factorization of a number, we need to identify which prime numbers multiply together to equal that number. We can use the factor pairs of a number to do this by starting with the smallest factor pair and dividing each number in the pair by the smallest prime number that divides it evenly. This process can be repeated until we are left with only prime numbers.

For example, to find the prime factorization of 21, we can start with the smallest factor pair, which is (1, 21). The smallest prime number that divides 1 evenly is 2, but 1 is not divisible by 2. The smallest prime number that divides 21 evenly is 3, so we divide 21 by 3 to get a quotient of 7 and a remainder of 0. This means that 3 is a factor of 21. We can then divide 7 by 3 to see if it is also divisible by 3. This gives us a quotient of 2 and a remainder of 1, which means that 7 is not divisible by 3.

**This means that the prime factorization of 21 is 3 x 7.**

I hope this helps! Let me know if you have any other questions.

## More factors

## Factors of 21 – Quick Recap

**Factors of 21:**1, 3, 7, and 21.**Negative Factors of 21:**(-1, -21) and (-2, -4).**Prime Factors of 21:**3 × 7**Prime Factorization of 21:**3 × 7

## Factors of 21 – Fun Facts

- 21 is a composite number, which means that it is not a prime number and it has more than two factors.
- The factors of 21 are the numbers that divide into 21 evenly (without a remainder). The factors of 21 are 1, 3, 7, and 21.
- 21 is the smallest number that is the product of two different prime numbers (3 and 7).
- The sum of the factors of 21 is 32 (1 + 3 + 7 + 21 = 32).
- 21 is the fifth triangular number, which means that it is the number of dots that can be arranged in an equilateral triangle. The first four triangular numbers are 1, 3, 6, and 10.
- 21 is the atomic number of scandium, a chemical element on the periodic table.
- 21 is also the number of cards in a blackjack hand.

**Also Check**: Multiples, Square Root, and LCM

## Solved Examples of Factor 21

**Q.1: What is the greatest common factor (GCF) of 21? **

Solution**:** The greatest common factor (GCF) of 21 is 3; it’s the largest number by which both can be divided without a remainder.

**Q.2:**How many factors does 21 have?** Solution:** Twenty-one has four different factors; these include 1, 3, 7, and 21.

** Q.3 Find three prime numbers whose product equals sixty-three when multiplied together.Solution:** Three prime numbers whose product equals sixty-three when multiplied together are 3, 3, and 07; 3x3x7= 63.

** Q.4: Is 18 a multiple or factor of 21?Solution: **18 is a multiple but not a factor of twenty-one as it cannot be divided evenly with no remainder (18/21 =0.8571428571).

** Q.5: Ashley needs to divide an equation into equal parts however each part must be divisible by seven; what equation could she use?Solution:** Ashley could use 28×4=112 as this equation can be divided into two equal parts both divisible by seven (112/7 = 16 & 112/16 = 7).

** Q.6: How many odd numbers remain between 1-21 when all even numbers are removed?Solution: **Nine odd numbers remain between one and twenty-one when all even numbers are removed; these would include 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19.

**Q.7:****Find two prime numbers that can only be divided evenly by themselves and one to generate a product that totals thirty-one. Solution: **Two prime numbers that can only be divided evenly by themselves and one to generate a product that totals thirty-one are 31 & 1; 31×1=31 and neither can be divided evenly with another number apart from themselves or one in order to equal thirty-one.

** Q.9: If there are five unequal numbers multiplied together which is the greatest possible total if their product equals seventy-five?Solution: **The greatest possible total if five unequal numbers multiplied together equal seventy-five is 15; 1x3x5x7x15=75.

** Q.10:How many pairs of factors are needed in order to multiply together in order to generate ninety?Solution: **Two pairs of factors need multiplying together in order to generate ninety; these would include 9×10=90 & 5×18=90.

** Q.11: What two consecutive odd numbers add up to twenty while their product remains divisible by seven?Solution: **Two consecutive odd numbers adding up to twenty while keeping their product divisible by seven are 9 & 11 (9+11 = 20 & 9×11 = 99); 99/7 = 14.

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## Frequently Asked Questions on Factors of 21

**What is the greatest common factor (GCF) of 21?**

The greatest common factor (GCF) of 21 is 3; it’s the largest number and both can be divided without a remainder.

**How many factors does twenty-one have?**

Twenty-one has four different factors; these include 1, 3, 7, and 21.

**How many odd numbers remain between 1-21 when all even numbers are removed?**

Nine odd numbers remain between one and twenty-one when all even numbers are removed; these would include 1, 3, 5, 7, 9, 11, 13, 15, and 19.

**Find two prime numbers that can only be divided evenly by themselves and one to generate a product that totals eighty-one.**

Two prime numbers that can only be divided evenly by themselves and one to generate a product that totals eighty-one are 81 & 1; 81×1=81 and neither can be divided evenly with another number apart from themselves or one in order to equal eighty-one.

**If there are five unequal numbers multiplied together which is the greatest possible total if their product equals seventy-five?**

The greatest possible total if five unequal numbers multiplied together equal seventy-five is 15; 1x3x5x7x15= 75.

**Is 18 a multiple or a factor of 21?**

18 is a multiple but not a factor of twenty-one as it cannot be divided evenly with no remainder (18/21 = 0.8571428571).

**How many pairs of factors are needed in order to multiply together in order to generate ninety-nine?**

Two pairs of factors need multiplying together in order to generate ninety-nine; these would include 9×11=99 & 3×33=99.

**Find three prime numbers which multiplied together and **generate a product that is divisible by seven.

Three prime numbers multiplied together to generate a product that is divisible by seven are 3, 5, and 7; 3x5x7= 105 and 105/7=15.

**Danny needs to reduce an equation by half but keep it divisible by seven; what equation could he use?**

Danny could use 14×2=28 as this equation can be reduced by half while still staying divisible by seven (14/2=7 and 28/7=4).

**What two consecutive odd numbers add up to twenty-six while their product remains divisible by seven?**

Two consecutive odd numbers adding up to twenty-six while keeping their product divisible by seven are 13 & 15 (13+15 = 28 & 13×15 = 195); 195/7 = 27.

Written by by

Prerit Jain