Deficient number checker

Client

Deficient numbers are the default—almost all integers have proper divisors summing below n. Confirm quickly for puzzles or proofs.

About Deficient number checker

Check whether proper divisors sum to less than n—most primes and powers of two are deficient. The interactive transform on this page runs in your browser tab—Toolcore does not need your paste for the core operation described above.

How to use this page

Paste or type in the main workspace, run the primary action from the toolbar, then copy or download the result. Use Load example when the page offers it, or URL prefill (?q= / ?qb=) so agents and tickets open the same input.

7 is deficient (sum 1).

Nearby workflows on Toolcore

  • Abundant number checker — See if a number is abundant—proper divisors sum to more than n—computed in-browser. when units or numeric output should be checked on a related calculator.
  • Perfect number checker — Test whether n equals the sum of its proper divisors (6, 28, 496, …)—runs locally up to safe integer limits. when units or numeric output should be checked on a related calculator.
  • Prime number checker — Test whether a whole number is prime—BigInt trial division in your browser, no upload. when units or numeric output should be checked on a related calculator.
  • Math expression evaluator — Evaluate basic + − × ÷ arithmetic with parentheses in your browser—no variables. when units or numeric output should be checked on a related calculator.

Common use cases

  • Verify that a prime is deficient by inspection.
  • Compare abundance classes in the same worksheet.

Common mistakes to avoid

  • Calling 1 deficient without context

    This tool treats 1 separately—no proper divisors exist.

FAQ

Are all primes deficient?

Yes—for p>1 the proper divisor sum is 1 < p.

More tools

Related utilities you can open in another tab—mostly client-side.