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Number Theory and Divisibility
Divisibility rules, factors, multiples, GCF, LCM, primes and modular ideas.
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67 cards
- Divisible by 2 ifQuestionThe last digit is even (0, 2, 4, 6, 8)
- Divisible by 3 ifQuestionThe sum of the digits is divisible by 3
- Divisible by 4 ifQuestionThe last two digits form a number divisible by 4
- Divisible by 5 ifQuestionThe last digit is 0 or 5
- Divisible by 6 ifQuestionIt is divisible by both 2 and 3
- Divisible by 8 ifQuestionThe last three digits form a number divisible by 8
- Divisible by 9 ifQuestionThe sum of the digits is divisible by 9
- Divisible by 10 ifQuestionThe last digit is 0
- Divisible by 11 ifQuestionThe alternating sum of the digits is divisible by 11
- Is 2,346 divisible by 3?QuestionYes, digit sum 15
- Is 4,125 divisible by 9?QuestionNo, digit sum 12
- Is 1,716 divisible by 4?QuestionYes, 16 is divisible by 4
- Is 121 divisible by 11?QuestionYes: 1 − 2 + 1 = 0
- Factors of 12Question1, 2, 3, 4, 6, 12
- Factors of 24Question1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36Question1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 48Question1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 60Question1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 100Question1, 2, 4, 5, 10, 20, 25, 50, 100
- Prime factorization of 12Question2² × 3
- Prime factorization of 36Question2² × 3²
- Prime factorization of 60Question2² × 3 × 5
- Prime factorization of 100Question2² × 5²
- Prime factorization of 72Question2³ × 3²
- Prime factorization of 84Question2² × 3 × 7
- Prime factorization of 90Question2 × 3² × 5
- Prime factorization of 120Question2³ × 3 × 5
- Prime factorization of 144Question2⁴ × 3²
- GCF of 12 and 18Question6
- GCF of 24 and 36Question12
- GCF of 15 and 25Question5
- GCF of 48 and 72Question24
- GCF of 17 and 31Question1 (both prime)
- LCM of 4 and 6Question12
- LCM of 6 and 8Question24
- LCM of 3 and 5Question15
- LCM of 9 and 12Question36
- LCM of 10 and 15Question30
- Relationship of GCF and LCMQuestionGCF(a, b) × LCM(a, b) = a × b
- Coprime (relatively prime)QuestionTwo numbers whose only common factor is 1
- Euclidean algorithmQuestionFind the GCF by repeatedly replacing the larger number with the remainder
- Sieve of EratosthenesQuestionA method that crosses out multiples to find primes
- Fundamental theorem of arithmeticQuestionEvery integer above 1 has exactly one prime factorization
- Largest prime factor ideaQuestionTest divisors only up to the square root
- Number of factors of a primeQuestion2
- Is there a largest prime?QuestionNo. Euclid proved there are infinitely many primes
- Is 97 prime?QuestionYes
- Is 101 prime?QuestionYes
- Is 111 prime?QuestionNo: 3 × 37
- Is 143 prime?QuestionNo: 11 × 13
- Is 221 prime?QuestionNo: 13 × 17
- Remainder of 17 ÷ 5Question2
- 17 mod 5Question2
- Modular arithmeticQuestionArithmetic where numbers wrap around after reaching a set value
- Clock arithmetic exampleQuestion5 hours after 10 o'clock is 3 o'clock (15 mod 12)
- Even + evenQuestionEven
- Odd + oddQuestionEven
- Odd + evenQuestionOdd
- Odd × oddQuestionOdd
- Even × any integerQuestionEven
- Sum of the first n odd numbersQuestionn²
- Sum of the first n whole numbersQuestionn(n + 1)/2
- Sum of 1 to 100Question5,050
- Goldbach's conjectureQuestionEvery even number above 2 is the sum of two primes (unproven)
- Fermat's Last TheoremQuestionNo positive integers satisfy aⁿ + bⁿ = cⁿ for n above 2; proved in 1994-95
- Pythagorean tripleQuestionThree whole numbers a, b, c with a² + b² = c²
- Common Pythagorean triplesQuestion3-4-5, 5-12-13, 8-15-17, 7-24-25
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