Factors Studio
Uncover the hidden building blocks of numbers. Visualize factor pairs with our Rainbow Tool and calculate factors instantly.
The Rainbow of Factors
Enter a number to see its factor pairs connected by rainbow arcs. Outer pairs connect to inner pairs!
The Power of Factors
Factors are the "ingredients" that multiply together to create a number. Understanding them helps you master fractions, division, and algebra.
The Rainbow Method
As shown in our visualizer, factors always come in pairs (except for the middle of a perfect square). Connecting them creates a beautiful rainbow shape.
Perfect Numbers
Some numbers are "Perfect". The number 6 is the smallest. Adding its factors (1+2+3) gives 6. It's a rare mathematical jewel.
Simplifying Fractions
To simplify 24/36, list factors for both.
24: 1, 2, 3, 4, 6, 8, 12, 24
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Largest match is 12! Divide both by 12 → 2/3.
Factors of 1 to 100
Use the table above to quickly reference factors for homework checks. Note which numbers have only two factors—those are the Primes!
Frequently Asked Questions
What is a 'Factor'?
A factor is a number that divides another number evenly, leaving no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 exactly.
How do I find all factors of a number?
Start with 1 and the number itself. Then check 2, 3, etc. Use the 'Rainbow Method' to find pairs by working from the outside in. If you find one factor (like 3 for 12), you automatically find its pair (4).
What is a Factor Pair?
A factor pair is a set of two numbers that multiply together to give your target number. For 12, the pairs are (1,12), (2,6), and (3,4).
What is a 'Perfect Square'?
A perfect square (like 36) has an odd number of factors. This is because one factor pairs with itself (6 x 6 = 36), so it doesn't have a distinct partner.
What is a 'Perfect Number'?
A perfect number is a number where the sum of its factors (excluding itself) equals the number. 6 is perfect (1+2+3 = 6). 28 is also perfect.
What is the Greatest Common Factor (GCF)?
The GCF is the largest factor shared by two numbers. It is crucial for simplifying fractions. For 12 and 16, the factors are (1,2,3,4,6,12) and (1,2,4,8,16). The largest shared one is 4.
Why is 1 a factor of every number?
Because any number divided by 1 is itself. 1 is the 'universal factor'.
Is the number itself a factor?
Yes! Every number is a factor of itself. For example, 10 is a factor of 10 (10 ÷ 10 = 1).
What are the factors of a Prime Number?
A prime number has exactly two factors: 1 and itself. That's the definition of a prime number.
How are factors used in real life?
Factors are used in arranging items (rows and columns), dividing pizzas, scheduling (time slots), and cryptography.