Random Prime Factorization Exercise Generator

Generate positive-integer factorization questions with prime factors and prime/composite answer metadata.

Description

Sample integers from 2 through a chosen maximum and return their prime factors and primality flag.

Prime factorization expresses an integer greater than one as a product of prime numbers, retaining repeated prime factors. A prime number therefore has a single factor in that list: itself.^[1]

Each item in result.exercises contains value, factors, and isPrime. The value is the learner’s question and the other fields supply its answer. The tool samples all integers in the range rather than balancing prime and composite questions.

When to use Random Prime Factorization Exercise Generator

Use it for prime-factorization practice or small integer fixtures with an included factor list.

How to use Random Prime Factorization Exercise Generator and understand its results

Enter integer exerciseCount from 1 through 64 and integer maximumValue from 2 through 1,000,000,000,000.
Run and read each value. Keep factors and isPrime separate when presenting a learner-facing question.
Check a response against the factor list, retaining multiplicities. Choose a modest maximum for quick interactive practice.

value = 2 + floor(randomDraw × (maximumValue − 1))

One draw per exercise samples inclusive integers from 2 through the maximum.

The prime-factorization calculator divides out factors of two, then tests odd divisors while their square does not exceed the remaining value. A final remaining value above one is appended. The generator sets isPrime when the resulting list has exactly one entry.

json

{
  "input": {
    "exerciseCount": 3,
    "maximumValue": 1000
  },
  "randomDraw": 0.25,
  "output": {
    "result": {
      "exercises": [
        {
          "value": 251,
          "factors": [
            251
          ],
          "isPrime": true
        },
        {
          "value": 251,
          "factors": [
            251
          ],
          "isPrime": true
        },
        {
          "value": 251,
          "factors": [
            251
          ],
          "isPrime": true
        }
      ]
    }
  }
}

Maximum two always gives value two. Powers of primes include repeated factors, such as [2, 2, 2] for eight. One, zero, negative values, and fractions are not generated. Bounds below two, counts above 64, and invalid draws fail.

Limitations and assumptions

The default source is Math.random; no seed input or cryptographic entropy guarantee is provided. Repeated runs may select the same result, and the distribution depends on the random source.

There is no prime/composite quota, uniqueness rule, difficulty filter, or cryptographic prime generation. Answers are returned openly.

Trial division takes longer for larger values with no small factors. A high maximum and many exercises can require substantially more work than a small classroom range.

Alternative or Complementary methods

Use factorization on a specific integer when a generated question is unnecessary. A primality checker answers only whether a chosen integer is prime.

References

Prealgebra 2e: Prime Factorization and the Least Common Multiple — OpenStax, Rice University

Similar or alternative tools

Prime Factorization
Factor a supplied integer and retain prime multiplicities.
Prime Checker
Check whether a supplied integer is prime.