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Instantly identify prime, composite, or special numbers. Supports batch checking and mathematical property analysis.
Enter a number to check
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself. A composite number is greater than 1 and has additional positive factors. The number 1 is neither because it has only one positive factor. This checker evaluates one positive whole number and, for values above 1, shows its classification, factor count, prime factorization, and complete list of positive factors.
For example, 17 is prime because its only positive factors are 1 and 17. The number 18 is composite: its factors include 2, 3, 6, and 9 in addition to 1 and 18. OpenStax uses the same distinction between primes, composites, and 1.
The factor list answers which positive whole numbers divide the input evenly. Prime factorization answers a different question: which prime numbers multiply to make the input. For 60, the full factor list is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60; the prime factorization is 2 × 2 × 3 × 5. Multiplying the prime factors returns 60.
A prime appears in its own prime factorization, so 17 is shown as 17. Repeated factors matter: 36 is 2 × 2 × 3 × 3, not merely 2 × 3. The count of all factors is the number of entries in the displayed positive-factor list.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Use a single integer such as 17, 36, or 60. The result updates from that one input; this page is not a multi-number batch checker.
The main result labels the value prime, composite, or neither. For 1, the page gives the neither result and does not show ordinary factorization details.
For values above 1, count the positive factors and multiply the prime factors. A prime has two positive factors; a composite has more than two.
Use the copy control to copy the classification and factor details, or clear the input before checking another integer.
Try 60 as a worked check: 2 × 2 × 3 × 5 = 60, and the factor list contains 12 entries. For 97, the only entries are 1 and 97, so it is prime.
Use cases
See how the tool fits into real work and everyday tasks.
Enter the original integer, compare the prime-factor list with your factor tree, then multiply the listed primes to confirm they reconstruct the original value.
Use the complete factor list to see possible equal group sizes for a positive number of items. For 18 items, factors such as 2, 3, 6, and 9 correspond to even groupings.
Q&A
Find concise answers to common questions and confusing cases.
A prime has exactly two positive factors, while 1 has only one. It also cannot be expressed as a product of two whole numbers greater than 1.
Two has exactly the positive factors 1 and 2. Every larger even whole number is divisible by 2 as well as 1 and itself, so it is composite.
No. It lists positive factors only. For example, the list for 12 contains 1, 2, 3, 4, 6, and 12.
Notes
Review scope, result limitations, and important precautions before use.
Use one positive whole number. Zero and negative values do not produce a classification, and decimals or text are not valid whole-number inputs. Very large values can take longer to process; independently verify results when exact arithmetic is important. The displayed factors are positive factors, not every integer divisor.
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