What Is a Factor Calculator?
A factor calculator is an online math tool that helps you find all factors of a number. A factor is a number that divides another number evenly with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of those numbers divides 12 evenly.
This factors calculator is designed for students, parents, teachers, and anyone who needs quick math homework help. It works as a factor pairs calculator, prime factorization calculator, prime factor calculator, factor tree calculator, greatest common factor calculator, GCF calculator, LCM calculator, and common factors calculator in one simple page.
How to Use the Factor Calculator
To use the factor calculator, enter a whole number such as 12, 24, 36, or 100. Then click the “Calculate Factors” button. The calculator will show the factors of a number, factor pairs, prime factorization, exponent form, and helpful number facts such as whether the number is prime, composite, even, odd, or a perfect square.
You can also choose “Show negative factors” if your class is learning about negative factor pairs. When this option is selected, the calculator includes negative factors such as -1 and -12 for the number 12. The product of two negative numbers is positive, so negative factor pairs can also multiply to the original number.
What Is a Factor?
A factor is a whole number that divides another whole number evenly. If there is no remainder, then the divisor is a factor. For example, 4 is a factor of 24 because 24 ÷ 4 = 6. But 5 is not a factor of 24 because 24 ÷ 5 leaves a remainder.
Students often learn factors and multiples together. Factors are numbers that divide into a number. Multiples are numbers you get when you multiply a number by 1, 2, 3, 4, and so on.
How to Find Factors of a Number
To find all factors, start with 1 and test each whole number up to the square root of the number. If the number divides evenly, then both the divisor and the matching quotient are factors. This calculator uses that efficient method, so it can find all factors quickly.
Example: To find all factors of 36, test whole numbers that divide 36 evenly. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
What Are Factor Pairs?
Factor pairs are two numbers that multiply together to make the original number. A factor pairs calculator is helpful because it shows the multiplication relationship clearly.
Factor pairs of 12: 1 × 12, 2 × 6, 3 × 4
Factor pairs of 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6
Factor pairs of 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
What Is Prime Factorization?
Prime factorization means writing a number as a product of prime numbers. A prime number has exactly two positive factors: 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are prime numbers.
A prime factorization calculator helps students break a composite number into prime factors. This is similar to using a factor tree calculator. For example, 36 can be broken into 2 × 2 × 3 × 3. In exponent form, that is 2² × 3².
Prime Numbers vs Composite Numbers
A prime number has exactly two positive factors: 1 and the number itself. For example, 13 is prime because its only positive factors are 1 and 13. A composite number has more than two positive factors. For example, 36 is composite because it has several factors, including 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The number 1 is neither prime nor composite. It has only one positive factor, which is 1.
What Is the Greatest Common Factor?
The greatest common factor, often called the GCF, is the largest factor shared by two or more numbers. A greatest common factor calculator or GCF calculator is useful when simplifying fractions, solving ratio problems, and comparing groups.
Example: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The common factors are 1, 2, 3, 4, 6, and 12. The GCF is 12.
What Is the Least Common Multiple?
The least common multiple, or LCM, is the smallest positive number that two or more numbers can divide into evenly. An LCM calculator is helpful for adding and subtracting fractions with different denominators, working with schedules, and solving multiples problems.
For example, the LCM of 24 and 36 is 72 because 72 is the smallest positive number that both 24 and 36 divide evenly.
Difference Between Factors and Multiples
Factors divide into a number evenly. Multiples are the answers you get when you multiply a number by whole numbers. For example, 3 is a factor of 12 because 12 ÷ 3 = 4. Multiples of 3 include 3, 6, 9, 12, 15, and 18.
A good way to remember the difference is this: factors are usually smaller than or equal to the number, while multiples are usually greater than or equal to the number.
Common Factor Examples
Common factors are factors shared by two or more numbers. This common factors calculator section helps you list the factors of each number and compare them.
Common factors of 12 and 24: 1, 2, 3, 4, 6, 12
Common factors of 24 and 36: 1, 2, 3, 4, 6, 12
Common factors of 18 and 30: 1, 2, 3, 6
Why This Calculator Is Helpful for Students
This math factor calculator is helpful because it does more than give a final answer. It also shows factor pairs, prime factorization, exponent form, and step-by-step reasoning. This helps students understand how the answer was found instead of only copying a result.
Teachers can use the tool to create examples for class. Parents can use it to check homework. Students can use it to practice factors and multiples, prime and composite numbers, GCF, LCM, and prime factorization.
Factor Calculator Examples
Factors of 12
Factors of 12: 1, 2, 3, 4, 6, 12
Factor pairs of 12: 1 × 12, 2 × 6, 3 × 4
Factors of 24
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factor pairs of 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6
Factors of 36
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Prime factorization of 36: 2² × 3²
