Number Theory Homework Help
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Number Theory questions
- Convert 1110 base 2 to base 10
- A packet contains number cards. Sally picked cards with numbers 2, 4, 5 and 9 from the packet. Which of the following…
- If 3245six = xnine, find x. Convert 101.01two to base ten. Solve (x+2)/3 = 5.
- The set E, F and G are defined as E=(odd numbers less than 13), F= ( multiples of 3 less than 15 and G=(multiples of 5…
- Write the first 10 multiples of the following: 12, 20, 50, 15, 6, 25, 8, 9, 7, 13
- Find the factors of the following numbers: a. 40 (k) 96 (c) 75 (d) 180 (e) 104
- Find the LCM using the multiple of vector. 16 and 27, 210 and 20. Find the H.C.F. 3, 5, 10, 15, 4) 9, 12. Change the…
- Write down three prime factor and their factors
- What is the least common multiple of 18 and 16 with the prime factors method
- Divide the LCM of 96,36 and 60 by their HCF
- What is the smallest number that can be divided by 8 and 12 without a remainder?
- Prove by mathematical induction that for all positive integers, n, 10ⁿ + 3 × 4^(n+1) + 5 is divisible by 3.
- Divide the LCM of 160,18,24 by their HCF
- Find the HCF and LCM of 9, 6, and 8. Divide the LCM of 160, 18, 21
- Given the polynomial g(x) = 3x³ − 7x² + 3x − 5x − 1, find the remainder and quotient when g(x) is divided by (x² − 2x…
- The set G=0, 1, 2. Define the composition + on G, for any a, b ∈ G by a + b = c where c is the least non-negative…
About Number Theory
Number theory is the study of whole numbers: what divides what, which numbers are prime, what remainders do, and how numbers behave in bases other than ten. In school it is where prime factorisation, HCF and LCM, divisibility tests and modular arithmetic live, and it is unusually rewarding because most questions can be checked by hand once the answer is found.
Popular topics in Number Theory
Prime Factorisation
Expressing a number as a product of primes, factor trees, and reading HCF and LCM off the factorisations.
HCF & LCM
Highest common factor and lowest common multiple, and the word problems (bells, taps, tiles) that hide one of them.
Divisibility
Tests for 2, 3, 4, 5, 6, 8, 9 and 11, proving divisibility, and finding what to add or subtract to make a number divisible.
Factors & Multiples
Listing factors, counting them, perfect squares, and the difference between a factor and a multiple.
Number Bases
Converting between base ten and bases two, five, eight and sixteen, and arithmetic performed inside a base.
Modular Arithmetic
Remainders, congruence, multiplication tables in a modulus, and repeating patterns of powers.
Primes & Composites
Identifying primes, the sieve of Eratosthenes, twin primes, and why 1 is neither prime nor composite.
Sequences of Integers
Triangular and square numbers, the Fibonacci sequence, and finding a rule from a pattern of terms.
How ScanSolve helps with Number Theory
ScanSolve shows the factor tree or the division algorithm rather than jumping to an answer, so an HCF or LCM question ends with working you can verify. For base conversions the place values are written out — 3425 in base five is 3x125 + 4x25 + 2x5 + 5 — which is what makes the method transferable to any base.
Remainder and divisibility questions are answered with the rule named and applied, and where a proof is wanted ("show that 7^n - 1 is divisible by 6") the induction or factorisation is set out in full. Every answer can be checked by multiplying back, and the check is included.
Study tips for Number Theory
- 01
Learn the divisibility tests for 3, 4, 8, 9 and 11. They turn a long division into a glance.
- 02
For HCF and LCM, write both numbers as products of primes first. After that, HCF takes the lowest power of each shared prime and LCM the highest.
- 03
In base arithmetic, write the place values above the digits. Confusion in base questions is almost always about place value, not arithmetic.
- 04
Check your answer by reversing the operation: multiply the factors back, or convert your base answer to base ten and compare.
Frequently asked Number Theory questions
How can ScanSolve help with Number Theory homework?
ScanSolve's AI solves number theory problems step by step. Snap a photo of your homework or type your question to get instant, detailed solutions with clear explanations.
Is Number Theory homework help free on ScanSolve?
Yes, ScanSolve offers free number theory homework help with step-by-step solutions. Upgrade to Pro at $89.99/year (about $7.50/month) or $9.99/week for unlimited answers and our most capable AI model.
What Number Theory topics does ScanSolve cover?
ScanSolve covers all number theory topics including Prime Factorisation, HCF & LCM, Divisibility, Factors & Multiples, Number Bases. Upload any number theory problem and get a step-by-step solution.
Can ScanSolve solve number theory problems from a photo?
Yes. Take a photo of your number theory homework and ScanSolve's AI will read the problem, identify the method needed, and provide a complete step-by-step solution.
How accurate are ScanSolve's number theory solutions?
ScanSolve uses advanced AI to deliver accurate, step-by-step number theory solutions. Each answer includes detailed explanations so you can verify the reasoning and learn the method.
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