Factor Calculator
A factor calculator helps you find the whole-number factors of a given number. Factors are numbers that divide another number evenly, leaving no remainder. Finding factors is useful in arithmetic, algebra, fractions, number theory, and problems involving divisibility.
What Is a Factor?
A factor is a whole number that divides another number exactly. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder.
Factors usually appear in pairs. For 12, the pairs are:
1 Γ 12 = 12
2 Γ 6 = 12
3 Γ 4 = 12
How to Find the Factors of a Number
To find the positive factors of a whole number, test numbers that could divide it evenly. If the division leaves no remainder, that number is a factor.
For example, to find the factors of 18:
18 Γ· 1 = 18
18 Γ· 2 = 9
18 Γ· 3 = 6
This gives the factor pairs 1 and 18, 2 and 9, and 3 and 6. Therefore, the positive factors of 18 are 1, 2, 3, 6, 9, and 18.
Factors and Prime Numbers
A prime number has exactly two positive factors: 1 and the number itself. For example, 13 is prime because it can only be divided evenly by 1 and 13.
A number with more than two positive factors is called a composite number. For example, 12 is composite because it has six positive factors.
Prime Factorization
Factors can also be used to break a composite number down into prime numbers. This process is called prime factorization.
For example:
60 = 2 Γ 2 Γ 3 Γ 5
So the prime factorization of 60 is 2Β² Γ 3 Γ 5. Prime factorization is useful for simplifying fractions, finding greatest common factors, and finding least common multiples.
Why Use a Factor Calculator?
Finding factors manually is easy for small numbers but can take more time when the number becomes larger. A factor calculator can quickly identify the factors and help you check your own work.
It can also be useful when working through problems involving divisibility, factor pairs, prime numbers, or factorization.
Common Mistakes to Avoid
Make sure the number is entered correctly and remember that a factor must divide the original number with no remainder. Do not confuse factors with multiples. Factors divide a number evenly, while multiples are produced by multiplying a number by whole numbers.
Factors vs. Multiples
For example, the factors of 6 are 1, 2, 3, and 6. Its multiples include 6, 12, 18, 24, and 30.
The key difference is simple: factors are numbers that divide a given number exactly, while multiples are numbers obtained by multiplying the given number by an integer.
Quick Summary
A factor is a whole number that divides another number without a remainder. A factor calculator can make it easier to find factor pairs, identify factors, and check results, especially when working with larger numbers.