Comprehensive Calculator Guide
This calculator writes any number up to a trillion as a product of primes with powers, such as 360 = 2³ × 3² × 5, with the repeated-division steps taught at school, the number of divisors and whether it is prime. Factorization gives GCDs, LCMs and simplified fractions and radicals.
Repeated division
Divide by the smallest prime that goes in, repeat, then move to the next prime until you reach 1. You only need primes up to the square root of what’s left. The number of divisors is the product of (each power + 1).
How to Use
- Enter a whole number above 1.
- Nothing else is needed.
- Press “Factorize” to see the factorization, the steps and the divisor count.
Formula Used
Divide by the smallest prime factor until the result is 1
Practical Examples
- Example 1
- 360 = 2³ × 3² × 5, 24 divisors.
- Example 2
- 1001 = 7 × 11 × 13, 8 divisors.
- Example 3
- 97 is prime.
Important Tips
- Always start with 2.
- Use divisibility rules.
- Write repeated factors as powers.
Common Mistakes to Avoid
- Stopping at a non-prime like 4.
- Writing 1 as a factor.
- Dividing out of order and losing factors.
Frequently Asked Questions
- What is 360 in prime factors?
- 2³ × 3² × 5.
- Is the factorization unique?
- Yes, by the fundamental theorem of arithmetic.
- How do I count divisors?
- Multiply (each power + 1).