Build animated factor trees for any integer. Shows unique prime factorization, GCD, LCM, and divisor count.
Type any integer and this tool grows a factor tree, splitting each composite node into a pair of factors until every leaf is prime, with each division animated as it happens. It then reports the unique prime factorization with exponents, the divisor count, and, for two numbers, the GCD and LCM derived from those exponents. The usual surprise: the tree you see is only one possible drawing. 360 can split first as 2 x 180 or as 18 x 20, and both are correct; only the multiset of prime leaves is unique.
A concrete input and expected output from the current implementation.
Input
360
Expected output
Animated tree: 360 -> 2 x 180 -> 2 x 90 -> 2 x 45 -> 3 x 15 -> 3 x 5. Unique prime factorization: 2^3 x 3^2 x 5. Divisor count: (3+1)(2+1)(1+1) = 24.
Each split divides the current value by its smallest prime factor: 360 halves three times, then divides by 3 twice, leaving 5. Grouping the six prime leaves by exponent gives 2^3 x 3^2 x 5, and the divisor count multiplies each exponent plus one: 4 x 3 x 2 = 24.
Every composite node splits into two factors whose product is the node's value, and the tool recurses on both children until a primality check stops the branch at a prime leaf. The animation plays the divisions in sequence, and the same number can yield different-looking trees depending on the first split. The leaves, collected and grouped by exponent, feed everything else the tool reports.
From the leaves the tool writes n as the product of p_i^e_i, with repeated primes grouped into exponents. The divisor count is the product of (e_i + 1) over all primes. For two numbers, the GCD takes the smaller exponent of each shared prime and the LCM the larger; the identity GCD x LCM = a x b always holds, which is a quick way to check the pair of answers.
Both, as long as every leaf is prime. The fundamental theorem of arithmetic guarantees the multiset of prime factors is unique; only the intermediate branch choices differ. Splitting 360 as 2 x 180 or as 18 x 20 ends at the same leaves, 2, 2, 2, 3, 3, 5, so the factorization 2^3 x 3^2 x 5 is identical either way.
A prime input never splits: the tree stays a single node and the divisor count comes out as 2, which is how you read primality from the result. How large an input the page accepts varies, and factoring slows as the largest prime factor grows, so very large numbers, especially semiprimes, can take a while or exceed the tool's limit.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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