Factors of 28 | Prime Factorization of 28 - Explained Simply

Today we are going to present here Factor Tree of 28. The factor is the number that divides the original number. The Factors of 28 are 1, 2, 4, 7, 14 and 28 itself.

What are the factors of 28?

The factors of 28 are all the whole numbers that, when divided into 28, result in a whole number with no remainder. We can also think of them as the whole numbers that multiply together to give 28.

Factor Tree Method of 28: Explained Simply

Finding factors is like playing a detective game. We'll start checking numbers from 1 upwards, seeing if they divide 28 evenly. When we find one, we've found a factor! And importantly, the result of that division will also be a factor.

Finding the Factors of 28 : Step-by-Step Method

Start with 1: Every number has 1 as a factor.

1 × 28 = 28

So, 1 and 28 are factors.

Try the next whole number (2):

28 ÷ 2 = 14

So, 2 and 14 are factors.

Try the next whole number (3):

28 ÷ 3 does not give a whole number (it's 9 with a remainder of 1).

So, 3 is not a factor.

Try the next whole number (4):

28 ÷ 4 = 7

So, 4 and 7 are factors.

Try the next whole number (5):

28 ÷ 5 does not give a whole number.

So, 5 is not a factor.

Try the next whole number (6):

28 ÷ 6 does not give a whole number.

So, 6 is not a factor.

Consider when to stop: We found the pair (4, 7). Notice that our next number to check would be 7, but we've already found 7 as a factor! This means we've found all the unique pairs, and we can stop. A quick trick is to stop when the number you are checking (e.g., 5, 6) is greater than the square root of 28 (which is approximately 5.29). Since 7 is greater than 5.29, and we already found 7, we're done!

The Complete List of Factors of 28

By following our step-by-step method, we have successfully identified all the factors of 28. Let's list them out clearly:

There are 6 factors for the number 28.

Factor Pairs of 28

Factors often come in pairs that multiply together to give the original number. For 28, these pairs are:

(1, 28)

(2, 14)

(4, 7)

Composite Factors of 28

A composite number is a whole number greater than 1 that has more than two factors. (Note: 1 is neither prime nor composite).

The composite factors of 28 are:

4 (factors: 1, 2, 4)

14 (factors: 1, 2, 7, 14)

28 (factors: 1, 2, 4, 7, 14, 28)

Sum of Factors of 28

If you add all the factors of 28 together:

1 + 2 + 4 + 7 + 14 + 28 = 56

A perfect number is a positive integer that is equal to the sum of its proper positive divisors (divisors excluding the number itself).

The proper divisors of 28 are 1, 2, 4, 7, 14.

Sum of proper divisors = 1 + 2 + 4 + 7 + 14 = 28.

Since the sum of its proper divisors equals the number itself, 28 is indeed a perfect number! This is a rare and fascinating property.

Prime Factorization of 28

Now, let's apply these concepts to find the prime factorization of 28 using two common methods.

The Division Method or Ladder Method

This method involves repeatedly dividing the number by the smallest possible prime numbers until the result is a prime number itself.

Start with the number 28.

Divide by the smallest prime number that divides 28 evenly. The smallest prime number is 2.

28 ÷ 2 = 14

Take the result (14) and repeat the process. Can 14 be divided by 2? Yes.

14 ÷ 2 = 7

Take the new result (7). Is 7 a prime number? Yes, it only has factors 1 and 7.

Stop when you reach a prime number.

Collect all the prime divisors used.

Visualizing the Division Method:

```

2 | 28

2 | 14

| 7

```

The numbers on the left (2, 2) and the final number at the bottom (7) are your prime factors.

The prime factors of 28 are 2, 2 and 7.

The Factor Tree Method

The factor tree method provides a visual way to break down a number into its prime factors.

Start with the number 28 at the top.

Find any two factors of 28 (besides 1 and 28) and draw branches to them.

Let's choose 4 and 7.

Check if these factors are prime:

Is 7 prime? Yes. (Circle it – it's a "leaf" of your tree).

Is 4 prime? No.

If a factor is not prime, break it down further into two more factors.

Break down 4 into 2 and 2.

Check if these new factors are prime:

Is 2 prime? Yes. (Circle it).

Continue this process until all the "leaves" of your tree are prime numbers.

Collect all the circled prime numbers.

Visualizing the Factor Tree Method:

```

/ \

⑦ 4

/ \

② ②

```

The circled numbers at the end of the branches (2, 2, 7) are your prime factors.

The prime factors of 28 are 2, 2 and 7.

Both methods lead to the same result!

The prime factorization of 28 is: 2 × 2 × 7

We can also write this in a more compact form using exponents, especially when a prime factor appears multiple times:

2² × 7 (read as "2 squared times 7")

This form clearly shows that 28 is built from two 2's and one 7.