Study Guide · Maths

What are the Factors of 54?

Finding the factors of a number means finding all the numbers that can cleanly divide into it with a remainder of exactly zero.

Question (Click to Flip)

What are the common factors of 54 and 27?

Answer

The factors of 27 are: 1, 3, 9, 27. The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54. The common numbers in both lists are 1, 3, 9, and 27. The Highest Common Factor (HCF) is 27.

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Key Facts

You can quickly check if a massive number is divisible by 3 using the 'Rule of 3'. Add the digits together (5 + 4 = 9). Since 9 is divisible by 3, you know immediately that 54 is divisible by 3.

You can tell 54 is not divisible by 5 because it does not end in a 0 or a 5.

1. What are the Factors of 54?

Because 54 is an even number with many divisors, it has exactly 8 positive factors. The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54.

2. How to Calculate the Factors

We find the factors by systematically dividing 54 by ascending numbers:

$54 \div 1 = 54$ (Factors: 1, 54)
$54 \div 2 = 27$ (Factors: 2, 27)
$54 \div 3 = 18$ (Factors: 3, 18)
$54 \div 4 = 13.5$ (No)
$54 \div 5 = 10.8$ (No)
$54 \div 6 = 9$ (Factors: 6, 9)
$54 \div 7 = 7.7$ (No)
$54 \div 8 = 6.7$ (No) Since the next number is 9, and we already have 9, we stop.

3. Factor Pairs of 54

If you multiply these pairs together, the result is always 54:

$1 \times 54 = 54$
$2 \times 27 = 54$
$3 \times 18 = 54$
$6 \times 9 = 54$

4. Prime Factorization of 54

To find the prime factorization, we divide by the smallest prime number (2):

$54 \div 2 = 27$
Now divide 27 by the next prime (3): $27 \div 3 = 9$
Divide 9 by 3: $9 \div 3 = 3$ The prime factorization of 54 is: $2 \times 3 \times 3 \times 3$ (or $2 \times 3^3$).

Questions and Answers

What are the common factors of 54 and 27?+

The factors of 27 are: 1, 3, 9, 27. The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54. The common numbers in both lists are 1, 3, 9, and 27. The Highest Common Factor (HCF) is 27.

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