Primality test by trial division
For any integer N, AskSia divides by primes 2, 3, 5, 7, 11 and so on up to the square root of N. If no prime divides evenly, N is prime. The trials are shown explicitly.
Trial division
AI Solver by AskSia
Prime Number Solver: test it, factor it, list them
Paste any integer to test primality, factor into primes, or list all primes up to a limit. AskSia uses trial division for primality, the factor tree for factorization, and the sieve of Eratosthenes for listing, with the method shown step-by-step.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is the AskSia Prime Number Solver?
AskSia's Prime Number Solver is an AI tool for three prime-related tasks. Primality test: AskSia checks if an integer N is prime by trial division up to the square root of N. Prime factorization: AskSia writes N as a product of primes using a factor tree. Prime list: AskSia generates all primes up to a given limit using the sieve of Eratosthenes. Each task shows the method explicitly, so the result is reproducible by hand for small cases.
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solution accuracy
50M+
problems solved
~1.5s
avg solve time
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study-ready explanations
Why AskSia Solver
Three prime tasks. One solver.
Test, factor, list. AskSia uses trial division, the factor tree, and the sieve, with the method shown so you can repeat the work yourself.
Factor tree for prime factorization
AskSia builds a factor tree: start with N, split into two factors, continue until all leaves are prime. The final factorization is the product of all leaves, with exponents collected.
Factor tree
Sieve of Eratosthenes for prime lists
To list primes up to N, AskSia starts with all integers from 2 to N, then strikes out multiples of 2, 3, 5, and so on. What remains is the list of primes.
Sieve method
GCF and LCM from prime factorization
Once two numbers are factored into primes, the GCF is the product of minimum exponents and the LCM is the product of maximum exponents. AskSia shows the side-by-side comparison.
GCF, LCM
Plain English explanation
Each result has a plain-English reason: 'N is prime because no prime up to sqrt(N) divides it evenly', 'N factors as 2^3 times 3 times 5'. Useful for understanding the why.
Explained
Works for large integers
Trial division works for integers up to about 10^12 quickly. For larger integers, AskSia uses faster primality tests (Miller-Rabin) and reports the result with the method named.
Large N
How It Works
Three taps to a prime answer.
Step 01
Paste a number or range
An integer to test or factor, or a range like '1 to 100' for a list of primes.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
Choose the task
Test primality, factor into primes, or list primes up to N. AskSia applies the matching method.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
See the result with method
Primality verdict with trial divisions, factor tree with factorization, or sieve table with the list. Generate practice on primes or factoring.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
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Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
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Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
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Calc
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Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Every prime task.
Test primality
Is 97 prime? AskSia divides by primes up to sqrt(97), which is about 9.85, so trials are 2, 3, 5, 7. None divide evenly, so 97 is prime.
Primality
Prime factorization
Factor 360 into primes. AskSia builds a factor tree: 360 = 2 * 180 = 2 * 2 * 90 = ... resulting in 2^3 times 3^2 times 5.
Factoring
GCF and LCM problems
Find the GCF and LCM of two integers. AskSia factors both, then computes minimum and maximum exponents for each prime.
GCF, LCM
List primes up to a limit
List all primes from 1 to 100, or 1 to 1000. AskSia runs the sieve and returns the complete list.
List primes
Number theory practice
Practice primality, factoring, and divisibility problems for math competitions, number theory courses, or general curiosity.
Number theory
Divisibility rules
Quick divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10, 11. AskSia explains the rule and shows it on the number you provide.
Divisibility
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
How does AskSia check if a number is prime?
AskSia uses trial division: for an integer N greater than 1, divide N by every prime from 2 up to the square root of N. If any prime divides N evenly, N is composite. If none do, N is prime. The square-root cutoff works because if N = a * b with a less than or equal to b, then a is at most the square root of N. For very large N, AskSia uses faster tests (Miller-Rabin probabilistic primality), which are extremely reliable in practice.
What is prime factorization?
Every integer greater than 1 can be written as a product of primes in exactly one way (up to order). This is the fundamental theorem of arithmetic. For example, 360 = 2 * 2 * 2 * 3 * 3 * 5, or written with exponents, 360 = 2^3 times 3^2 times 5. AskSia returns the factorization in exponent form.
How are GCF and LCM computed from prime factorization?
Factor both numbers into primes. For each prime that appears, the GCF takes the minimum exponent and the LCM takes the maximum exponent. For example, 12 = 2^2 times 3 and 18 = 2 times 3^2, so GCF = 2^1 times 3^1 = 6 and LCM = 2^2 times 3^2 = 36. AskSia shows the side-by-side comparison.
What is the sieve of Eratosthenes?
An efficient method to list all primes up to N. Start with 2 and mark every multiple of 2 (above 2 itself) as composite. Move to the next unmarked number (3) and mark every multiple of 3. Continue up to the square root of N. Every remaining unmarked number is prime. AskSia shows the running sieve for small N so the elimination is visible.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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