Factors of 432

Prime numbers have exactly two factors, which are 1 and the number itself. Composite numbers have more than two factors. Now, let us learn more about the factors of 432.

Negative factors of 432: (-1, -432), (-2, -216), (-3, -144), (-4, -108), (-6, -72), (-8, -54), (-9, -48), (-12, -36), (-16,-27), (-18, -24)

Prime factors of 432: 2 and 3

Prime factorization of 432: 24 × 33

The sum of factors of 432: 1 + 2 +  3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 36 + 48 + 54 + 72 +108 +144 + 216 + 432 = 1240.
 

For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:

1. Use of Multiplication Method
2. Use of Division Method
3. Use of Prime Factors and Prime Factorization.

So, here we discuss a detailed explanation of the following methods:
 

So in the multiplication method, we will try to find out what numbers will multiply together, and give us the value 432. We will check the factors step by step:

Step 1: Start to multiply with numbers, which gives the value of 432.

Start with 1, and continue to multiply with other numbers. 

 1 ×  432  = 432
2  ×  216 = 432
3 ×  144 =  432
4 ×  108 =  432
6  ×  72 =  432
8  ×  54 =  432
9  ×  48 =  432
12 ×  36 = 432
16 ×  27 = 432
18 ×  24 = 432

Step 2: After the calculation, we get these numbers, the factors of 432.

Step 3: The positive factor pairs of 432 found through multiplication are (1, 432), (2, 216), (3,144), (4, 108) (6, 72), (8, 54), (9, 48), (12, 36), (16, 27), and (18, 24)

Step 4: The negative factor pairs of 432 are (-1, -432), (-2, -216), (-3,-144), (-4, -108) (-6, -72), (-8, -54), (-9,-48), (-12, -36)  (-16,-27), and (-18, -24)
 

Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 432:

Step 1: Divide 432 by smaller numbers and see if there is any remainder. E.g., 432/1 = 432. 

Step 2: We will continue in the same way and check for other numbers as well. For 432, the factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216 and 432 . Because 432 can be divided evenly by these numbers.

432 ÷ 2 = 216
432÷ 3 = 144
432÷ 4 = 108
432÷ 6 = 72
432÷8 = 54
432÷9 = 48
432÷12 =36
432÷16 = 27
432 ÷18 =24
 

By Using Prime Factorization: When using this method, the number is divided by its prime numbers until it is completely factored.

2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.

432 ÷ 2=216
216÷ 2=108
108 ÷ 2=54
54 ÷ 2=27
27 ÷ 3=9
9 ÷ 3=3
3 ÷ 3=1

The prime factorization of 432 is :432 = 2⁴ × 3³

Finally, using the prime factorization method, the prime factors of 432 are 2 and 3.
 

A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.

Step 1: 432 divided by 2 gives us the answer 216

Step 2: Since 216 is not a prime number, it can be divided further.

The prime factorization of 432 is written below : 432 = 2⁴ × 3³
 

Every number has either a positive or negative factor. Let us look at those sets of factors.

Positive pair Factors: (1, 432), (2, 216), (3,144), (4, 108) (6, 72), (8, 54), (9,48), (12, 36)  (16,27), (18, 24)
Negative pair Factors:  (-1, -432), (-2, -216), (-3,-144), (-4, -108) (-6, -72), (-8, -54), (-9,-48), (-12, -36)  (-16,-27), (-18, -24)
 

• Factors: The factors of numbers are complete numbers, that can be divided into another number evenly without remainder. Like 6 is divisible by 1, 2, 3, and 6, therefore, 1, 2, 3, and 6 are the factors of 6.

• Prime Factors: Prime numbers that divide a given number evenly. For 432, the prime factors are 2 and 3.

• Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).