Draw the Factor Tree of 20

Factors of 20

Factors of 20 are the list of integers that can be evenly divided into 20. It has a total of 6 factors of which 20 is the biggest factor and the positive factors of 20 are 1, 2, 4, 5, 10, and 20. The sum of all factors of 20 is 42. Its Prime Factors are 1, 2, 4, 5, 10, 20 and (1, 20), (2, 10) and (4, 5) are Pair Factors.

• Factors of 20: 1, 2, 4, 5, 10 and 20
• Negative Factors of 20: -1, -2, -4, -5, -10 and -20
• Prime Factors of 20: 2, 5
• Prime Factorization of 20: 2 × 2 × 5 = 2² × 5
• Sum of Factors of 20: 42

1.	What are Factors of 20?
2.	How to Calculate the Factors of 20?
3.	Factors of 20 by Prime Factorization
4.	Factors of 20 in Pairs
5.	Tips and Tricks
6.	FAQs on Factors of 20

What are Factors of 20?

A factor is a number that divides the number into equal parts. Factors of 20 are the numbers that divide 20 completely without leaving any remainder. 4 and 5 are the factors of 20, that is, 5 divides 20 into equal parts of 4 each.

20 does not have 4 and 5 as its only factors. It has other factors as well which we will show you in the next section.

How to Calculate the Factors of 20?

Follow the steps to calculate the factors of 20:

• Step 1: Write down the number to be factored, i.e., 20.
• Step 2: Find the numbers which can divide 20 exactly without leaving any remainder.
  • 20 ÷ 1 = 20 Remainder 0
  • 20 ÷ 2 = 10 Remainder 0
  • 20 ÷ 3 = 6 Remainder 2
• Step 3: Continue for rest of the numbers.

We see that 3 does not divide 20 completely and leaves a remainder. Therefore, 3 is not a factor. Continuing further, the numbers 1, 2, 4, 5, 10, and 20 leave no remainder. Hence, the factors of 20 are 1, 2, 4, 5, 10, and 20.

Important Notes:

1. Factors of a number are all the possible numbers it is divisible by.
2. They may be prime numbers or composite numbers.
3. Factors can never be fractions or decimals.
4. Factors can be negative integers.

Explore factors using illustrations and interactive examples

• Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
• Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
• Factors of 15 - The factors of 15 are 1, 3, 5, 15.
• Factors of 16 - The factors of 16 are 1, 2, 4, 8,16.
• Factors of 320 - The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320.
• Factors of 200 - The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.

Factors of 20 by Prime Factorization

Prime factorization is the process of writing a number as the product of its prime factors. Factors of 20 by prime factorization are found using the following steps:

Write the pair of factors that on multiplication gives the required number. 20 can be factored as a product of 4 and 5. Check the factors to see if each one of them is prime or not.

• Step 1: 4 is not a prime number and can be factored further as a 2 × 2.
• Step 2: 5 is a prime number and it cannot be factored further.
• Step 3: Prime factorization of 20 can thereby be written as: 20 = 4 × 5 = 2 × 2 × 5
• Step 4: It can also be written in exponent form as 20 = 2² × 5

Challenging Questions:

Jenny has an apple tree. She plucks 20 apples from the tree. She has to distribute it among her 4 friends. How many apples will each friend get?

Factors of 20 in Pairs

The pair of numbers that give 20 as the result when multiplied is the pair factors of 20. Let's try visualizing it using blocks:

The pair factors of 20 are:

Factors	Pair Factors
1 × 20 = 20	1,20
2 × 10 = 20	2,10
4 × 5 = 20	4,5
5 × 4 = 20	5,4
10 × 2 = 20	10,2
20 × 1 = 20	20,1

The above-given factors are positive pair factors. It is possible to have negative pair factors as well because the product of two negative numbers gives a positive number. Let's take a look at the negative pair factors of 20:

Factors	Pair Factors
-1 × -20 = 20	-1,-20
-2 × -10 = 20	-2,-10
-4 × -5 = 20	-4,-5
-5 × -4 = 20	-5,-4
-10 × -2 = 20	-10,-2
-20 × -1 = 20	-20,-1

Tips and Tricks:

1. The smallest factor of every number is 1.
2. Every number has a minimum of 2 factors, i.e. 1 and the number itself.
3. All even numbers have 2 as one of their factors.
4. All numbers which end in 5 will have 5 as one of their factors.
5. All numbers which end in 0 will have 1, 2, 5, and 10 as their factors.

Factors of 20 Solved Examples

1. Example 1: Four friends plucked 20 mangoes from a tree and distributed the fruits among themselves equally.

   How many would each one of them get?

   Solution:

   20 mangoes are to be divided among 4 friends equally. This implies that we need to divide 20 by 4 therefore 20 ÷ 4 = 5.

   Thus, each person will get 5 mangoes.

2. Example 2: A rectangle has an area of 20 square inches and a length of 10 inches. Determine its breadth.

   Solution:

   The area of the rectangle can be calculated by the formula: length × breadth. The length of the rectangle, i.e.,10 inches is a factor of the area, i.e., 20 square inches.

   When 2 is multiplied by 10, the product is 20 which can be written as 2 × 10 = 20. Thus, the breadth of the rectangle is 2 inches.

3. Example 3: How many factors are there for 20?

   Solution:

   The factors of 20 are 1, 2, 4, 5, 10, 20. Therefore, 20 has 6 factors.

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FAQs on Factors of 20

What are the Factors of 20?

The factors of 20 are 1, 2, 4, 5, 10, 20 and its negative factors are -1, -2, -4, -5, -10, -20.

How Many Factors of 20 are also Factors of 18?

Since, the factors of 20 are 1, 2, 4, 5, 10, 20 and the factors of 18 are 1, 2, 3, 6, 9, 18.
Hence, [1, 2] are the common factors of 20 and 18.

What are the Pair Factors of 20?

The pair factors of 20 are (1, 20), (2, 10), (4, 5).

What is the Sum of all the Factors of 20?

Since all factors of 20 are 1, 2, 4, 5, 10, 20 therefore, the sum of its factors is 1 + 2 + 4 + 5 + 10 + 20 = 42.

What is the Greatest Common Factor of 20 and 17?

The factors of 20 are 1, 2, 4, 5, 10, 20 and the factors of 17 are 1, 17. 20 and 17 have only one common factor which is 1. This implies that 20 and 17 are co-prime.

Hence, the Greatest Common Factor (GCF) of 20 and 17 is 1.

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Source: https://www.cuemath.com/numbers/factors-of-20/

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