Analyze any integer: even/odd, prime check, full prime factorization, all divisors, digit sum, digital root, binary/hex/octal representation, nearest primes, and number classification.
The **Integer Properties Calculator** is an all-in-one analysis tool for any integer. Enter a number and instantly see whether it is even or odd, prime or composite, along with its full prime factorization, complete list of divisors, digit sum, digital root, factor pairs, and classifications (perfect, abundant, or deficient).
The calculator also converts the number into **binary, octal, hexadecimal**, and any custom base from 2 to 36, with a visual bit-pattern display that color-codes each 1 and 0. A prime scanner lists all primes in a configurable range, highlighting your input if it appears in the list.
Preset buttons load interesting numbers: perfect squares like 1024, highly composite numbers like 360, large primes like 7919, and everyday values like 42. Whether you are studying number theory, debugging a bit-manipulation algorithm, or just curious about a number's properties, this calculator gives you a comprehensive report in seconds. It is most useful when you want the factor structure, divisor behavior, and base representations gathered in one place instead of checking them separately.
Finding all divisors, checking primality, and performing base conversions are tasks that each require a separate tool or manual work. This calculator combines them into a single page with visual aids (divisor chips, binary bit grid, factor badges) so you can explore a number's character without switching between windows.
It is especially helpful for students learning number theory: the factor pairs, prime factorization badges, and perfect/abundant/deficient classification are all concepts that appear in introductory courses but are tedious to compute by hand for large numbers.
Prime factorization: trial division up to √n. Divisor count: σ₀(n) = Π(eᵢ + 1) for prime factorization n = Πpᵢ^eᵢ. Digital root: 1 + ((n − 1) mod 9).
Result: 360 = 2³ × 3² × 5, 24 divisors, digit sum 9, abundant
360 is even, composite, with prime factorization 2^3 × 3^2 × 5. It has 24 divisors (including 1 and 360). The sum of proper divisors is 810 > 360, so it is abundant.
Every integer greater than 1 can be written as a unique product of primes (up to ordering). This calculator finds that product via trial division: repeatedly divide by the smallest prime that evenly divides the number until the quotient is 1. The factorization is displayed both as a compact expression (2³ × 3² × 5) and as individual prime-power badges.
Computers store integers in binary (base 2), and hexadecimal (base 16) is widely used in programming for memory addresses, color codes, and byte values. The visual bit-pattern grid in this calculator makes it easy to count leading zeros, identify powers of 2, and understand bitwise operations.
The sum of a number's proper divisors (all divisors except itself) classifies it as perfect (sum = n), abundant (sum > n), or deficient (sum < n). Perfect numbers are rare and deeply connected to Mersenne primes. Abundant numbers make up roughly 25% of positive integers, and the rest are deficient.
Repeatedly sum the digits until a single digit remains. For 942: 9+4+2 = 15 → 1+5 = 6. Shortcut: 1 + ((n−1) mod 9).
A perfect number equals the sum of its proper divisors. The first four are 6, 28, 496, and 8128.
Abundant: sum of proper divisors > n. Deficient: sum < n. Most integers are deficient.
Trial division up to √n, skipping multiples of 2 and 3. Efficient for numbers up to about 10^15.
Yes. The calculator analyzes |n| for divisors and factorization, and notes the sign separately.
It converts the number into any radix from 2 to 36, using digits 0–9 and letters A–Z. That makes it useful when you need to compare standard binary or hexadecimal output with a less common base for teaching or debugging.