Factors of 28

Factors of 28 are the list of integers that we can split evenly into 28. There are 6 factors of 28 of which 28 itself is the biggest factor and its positive factors are 1, 2, 4, 7, 14 and 28. The sum of all factors of 28 is 56. Its Prime Factors are 1, 2, 4, 7, 14, 28 and (1, 28), (2, 14) and (4, 7) are Pair Factors.

• Factors of 28: 1, 2, 4, 7, 14 and 28
• Negative Factors of 28: -1, -2, -4, -7, -14 and -28
• Prime Factors of 28: 2, 7
• Prime Factorization of 28: 2 × 2 × 7 = 2² × 7
• Sum of Factors of 28: 56

What are Factors of 28?

The factor of a number is that number that divides it completely without leaving any remainder. The number 28 is an even composite number i.e it is divisible by 2. The factors of 28 are pairs of those numbers whose product gives the value 28.

• Step 1: Write down the number to be factored, i.e. 28
• Step 2: Find the two numbers whose product gives 28
  • Let's say we take 2 and 14 as the numbers.
  • 2 is a prime number. Hence, it can only be factored as 1 and the number itself, i.e. 2
  • 2 can be written as 2 = 2 × 1
  • 14 is not a prime number. Hence, it can be factored as 2 and 7, apart from 1 and the number itself, i.e. 14
  • 14 can be written as 14 = 7 × 2 × 1

Hence, 28 can be factored as 28 = 7 × 2 × 2 × 1 which means that the Factors of 28 are 1, 2, 4, 7, 14, and 28

Important Notes:

• Factors of any number include all the possible numbers it is divisible by. They may be prime numbers or composite numbers. In this case, 28 is a composite number but 2 is a prime number.
• Factors are always whole numbers. They are never fractions or decimals. For example, even though the product of 56 and 0.5 is 28, they cannot be considered as factors of 28.

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 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
• Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128.
• Factors of 120 - The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
• Factors of 288 - The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

Writing a number as a product with all its factors being prime is called prime factorization. Let's learn how to find factors using prime factorization.

• Step 1: Write the pair of factors that on multiplication gives the required number.
• Step 2: Check the factors to see if each one of them is prime or not.
• Step 3: Follow the below criterion to differentiate between the factorization procedure.

1. If both the numbers are prime, they can be multiplied as it is.
2. If one among them is prime and the other is composite, then the composite number is dissociated into its factors.
3. If both the numbers are composite, they can be dissociated into factors.

Factors of 28 by prime factorization are given by using the following steps.

• Step 1:  28 can be factored as the product of 4 and 7.
• Step 2: 4 is not a prime number and can be dissociated as a product of 2 by itself or as a square of 2. 7 is a prime number. Hence, it doesn't need any further dissociation.
• Step 3: 28 can thereby be written as 28 = 4 × 7 = 2 × 2 × 7. The prime factors of 28 can also be written as 28 = 2² × 7. Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?

Factors of 28 in Pairs

Pair factors are pairs of those numbers which when multiplied give the required number as the product. Here, the required number is 28. Let's try visualizing it using blocks.

Positive pair factors of 28:

Negative pair factors of 28:

Tips and Tricks:

• 1 is the smallest factor of every number.
• 28 is an even number. Hence, 2 is one of its factors.