Factors of 27 - Definition, Examples, Quiz, FAQ, Trivia
Learn about factors, prime factorization, and factor pairs with clear explanations and practice activities
What are Factors?
Factors are numbers that divide evenly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 evenly.
When we multiply two numbers to get a product, those numbers are called factors of the product. For instance:
3 × 9 = 27, so 3 and 9 are factors of 27.
Every number has at least two factors: 1 and itself. Numbers with exactly two factors (1 and themselves) are called prime numbers. Numbers with more than two factors are called composite numbers.
Key Concept
A factor is a number that divides another number evenly with no remainder.
Factors of 27
The factors of 27 are the numbers that divide 27 exactly without leaving a remainder. Let's find them:
Step 1: Start with 1 and 27 (1 × 27 = 27)
Step 2: Check 2 (27 ÷ 2 = 13.5, not whole)
Step 3: Check 3 (27 ÷ 3 = 9, exactly)
Step 4: Check 4 (27 ÷ 4 = 6.75, not whole)
Step 5: Check 5 (27 ÷ 5 = 5.4, not whole)
Step 6: Check 6 (27 ÷ 6 = 4.5, not whole)
Step 7: Check 7, 8, 9 (27 ÷ 9 = 3, which we already have)
The complete list of factors of 27 is:
Since 27 has more than two factors (1, 3, 9, 27), it is a composite number.
Remember
27 is not a prime number because it has factors other than 1 and itself.
How to Find Factors of 27
There are two main methods to find factors of a number:
1. Division Method:
Divide 27 by all numbers from 1 to 27. If the division gives a whole number (no remainder), then both the divisor and the quotient are factors.
2. Multiplication Method:
Find pairs of numbers that multiply to give 27:
Multiplication Method
Find number pairs that multiply to 27:
The factors we get from these pairs are: 1, 3, 9, and 27.
Tip
You only need to check numbers up to the square root of 27 (about 5.2) since factors repeat after that point.
Prime Factorization of 27
Prime factorization is breaking down a number into its prime factors. Since 27 is 3 × 3 × 3, its prime factorization is:
Prime Factorization
We can represent this using a factor tree:
The prime factors of 27 are all 3s. This means 27 is a perfect cube since 3³ = 27.
Remember
Prime factorization breaks a number down to its smallest building blocks - prime numbers.
Factor Pairs of 27
Factor pairs are two numbers that multiply together to give the original number. For 27, we have:
Positive Factor Pairs:
Negative Factor Pairs:
The sum of all factors of 27 is 1 + 3 + 9 + 27 = 40.
Remember
Negative factors come in pairs just like positive factors - two negatives multiply to a positive.
Factors of 27 Quiz
Test your knowledge with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about factors:
Math Trivia
Discover interesting facts about numbers and factors:
Cube Number
27 is a perfect cube (3³ = 3 × 3 × 3 = 27). It's the first odd number that is a perfect cube and also the smallest cube that is not a square number.
Rubik's Cube
The original Rubik's Cube has 27 small cubes (3×3×3). Each face has 9 small squares, and there are 6 faces, totaling 54 stickers.
Prime Factors
27 has only one distinct prime factor: 3. This makes it a prime power. Numbers with a single prime factor are sometimes called "prime powers."
Sum of Factors
The sum of all factors of 27 is 1 + 3 + 9 + 27 = 40. This is called the "sum of divisors" in mathematics.
