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Factors of 432

Did you know 432 is known as Achilles number? It is among those numbers which also have square of prime factors as one its factor. For example, 2 and 4 are the factors of 432. In this mini lesson let us learn to calculate all the factors of 432, the factors of 432 in pairs and the prime factorization of 432. 

  • Factors of 432: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216 and 432
  • Prime Factorization of 432: 2 × 2 × 2 × 2 × 3 × 3 × 3 = 24 × 33  
1. What Are the Factors of 432?
2. How to Calculate the Factors of 432?
3. Factors of 432 by Prime Factorization
4. Factors of 432 in Pairs
5. Important Notes
6. Tips And Tricks
7. FAQs on Factors of 432

What are the Factors of 432?

The factors of 432 are the numbers that divide 432 completely without leaving any remainder. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24,  27, 36, 48, 54, 72, 108, 144, 216 and 432 are the factors of 432. 

How to Calculate the Factors of 432?

  • Determine half of 432. It is 216.
  • Using the divisibility rules, keep dividing 432 from 1 to 216. They form the divisors of 432. Obtain the quotient. 
  • The divisors and the quotient form the factors of 432.
  • While we are doing this, we observe that 432 is not divisible by 5, 7, 10, 11, 13, 14 and 15
  • While we are dividing by 18, we reach the level of obtaining all the factors of 432.
432 ÷ 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

To understand the concept of finding factors by prime factorization better, let us take a few more examples.

  • Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.
  • Factors of 108: The factors of 108 are 1, 2, 3 , 4, 6, 9, 12, 18, 27, 36, 54 and 108.
  • Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
  • Factors of 112: The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
  • Factors of 216: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.

Factors of 432 by Prime Factorization

We obtain the prime factors by using prime factorization.  This can be followed using factor tree or upside-division method.

  • Step 1: Divide 432 by its smallest prime factor 2. We get its composite factor-pair as 216.
  • Step 2: Divide 216 by its smallest prime factor, 2. The composite factor-pair is 108
  • Step 3: Keep dividing each time by the smallest prime factor and continue until we reach the level where no more factorization can be done.
  • This way we express 432 as a product of its prime factors 2 and 3. 
  • 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3 =  24 × 33

factors of 432 by prime factorization

Factors of 432 in Pairs

The factors that pair up to give the product 432 are the factors of 432 in pairs. We have 10 such distinct ordered pairs. They are (1, 432), (2, 216), (3, 144), (4, 108), (6, 72), (8, 54), (9, 48), (12, 36), (16,27) and (18, 24).

factors of 432 in pairs

Important Notes:

  • There are 20 factors of 432.
  • The prime factors of 432 are 2 and 3.
  • The prime factorization of 432 is 24 × 33.

Tips and Tricks

  • Do the prime factorization of 432 and obtain it as 24 × 33. Add 1 to each exponent and multiply them. Here we have (4+1) × (3+1) = 5 × 4 = 20.  This product helps us determine the total number of factors of 432.
  • Another trick is multiply 2 × 2 × 2 × 2 × 3 × 3 × 3 in all the possible ways to get the composite factors.
 

Factors of 432 Solved Examples

  1. Example 1: Andrew decides to buy 432 cars. He finds 2 packs at the wholesale shop. 216 toy cars at $18 and 432 toy cars at $36. Which is the better deal for him?

    Solution:

    Packs Number of Toy Cars Cost of the pack
    Pack 1 216 $18
    Pack 2 432 $36

    Let us determine the cost of each toy car in both the packs.
    We need to find the missing factor in each case.
    Cost of each toy car in pack 1 is 216 ÷ 18 = $12.
    Here the cost of 432 cars = $24
    Cost of each toy car in pack 2 is 432 ÷ 16 = $27
    $24 < $27. Therefore getting 2 packs of pack 1 is the better deal for Andrew.

  2. Example 2: If Amelia sent 432 messages in all in 18 days to her friend, find the messages that she had sent on an average in a day?

    Solution: 

    ___ of messages per day × 18 days = Total 432 messages
    ____ × 18 = 432
    Finding the missing factor-pair of 18 that makes 432, we find that 
    16 × 18 = 432
    Therefore, the number of messages sent on an average in a day = 16

Check Answer >

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FAQs on Factors of 432

What are the factors of 432?

The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24,  27, 36, 48, 54, 72, 108, 144, 216 and 432.

What factors of 432 sum up to 42 ?

The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24,  27, 36, 48, 54, 72, 108, 144, 216 and 432. The factors of 432 that sum up to 42 are 18 and 24.

What are the prime factors of 432?

The prime factors of 432 are 2 and 3.

What are the common factors of 432 and 420?

The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24,  27, 36, 48, 54, 72, 108, 144, 216 and 432. The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Hence, the common factors of 432 and 420 are 1, 2, 3, 4, 6 and 12.

What are the odd factors of 432?

The odd factors of 432 are 1, 3, 9 and 27.

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