#separator:tab #html:false #tags column:4 Divisible by 2 if The last digit is even (0, 2, 4, 6, 8) math-number-theory Divisible by 3 if The sum of the digits is divisible by 3 math-number-theory Divisible by 4 if The last two digits form a number divisible by 4 math-number-theory Divisible by 5 if The last digit is 0 or 5 math-number-theory Divisible by 6 if It is divisible by both 2 and 3 math-number-theory Divisible by 8 if The last three digits form a number divisible by 8 math-number-theory Divisible by 9 if The sum of the digits is divisible by 9 math-number-theory Divisible by 10 if The last digit is 0 math-number-theory Divisible by 11 if The alternating sum of the digits is divisible by 11 math-number-theory Is 2,346 divisible by 3? Yes, digit sum 15 math-number-theory Is 4,125 divisible by 9? No, digit sum 12 math-number-theory Is 1,716 divisible by 4? Yes, 16 is divisible by 4 math-number-theory Is 121 divisible by 11? Yes: 1 − 2 + 1 = 0 math-number-theory Factors of 12 1, 2, 3, 4, 6, 12 math-number-theory Factors of 24 1, 2, 3, 4, 6, 8, 12, 24 math-number-theory Factors of 36 1, 2, 3, 4, 6, 9, 12, 18, 36 math-number-theory Factors of 48 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 math-number-theory Factors of 60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 math-number-theory Factors of 100 1, 2, 4, 5, 10, 20, 25, 50, 100 math-number-theory Prime factorization of 12 2² × 3 math-number-theory Prime factorization of 36 2² × 3² math-number-theory Prime factorization of 60 2² × 3 × 5 math-number-theory Prime factorization of 100 2² × 5² math-number-theory Prime factorization of 72 2³ × 3² math-number-theory Prime factorization of 84 2² × 3 × 7 math-number-theory Prime factorization of 90 2 × 3² × 5 math-number-theory Prime factorization of 120 2³ × 3 × 5 math-number-theory Prime factorization of 144 2⁴ × 3² math-number-theory GCF of 12 and 18 6 math-number-theory GCF of 24 and 36 12 math-number-theory GCF of 15 and 25 5 math-number-theory GCF of 48 and 72 24 math-number-theory GCF of 17 and 31 1 (both prime) math-number-theory LCM of 4 and 6 12 math-number-theory LCM of 6 and 8 24 math-number-theory LCM of 3 and 5 15 math-number-theory LCM of 9 and 12 36 math-number-theory LCM of 10 and 15 30 math-number-theory Relationship of GCF and LCM GCF(a, b) × LCM(a, b) = a × b math-number-theory Coprime (relatively prime) Two numbers whose only common factor is 1 math-number-theory Euclidean algorithm Find the GCF by repeatedly replacing the larger number with the remainder math-number-theory Sieve of Eratosthenes A method that crosses out multiples to find primes math-number-theory Fundamental theorem of arithmetic Every integer above 1 has exactly one prime factorization math-number-theory Largest prime factor idea Test divisors only up to the square root math-number-theory Number of factors of a prime 2 math-number-theory Is there a largest prime? No. Euclid proved there are infinitely many primes math-number-theory Is 97 prime? Yes math-number-theory Is 101 prime? Yes math-number-theory Is 111 prime? No: 3 × 37 math-number-theory Is 143 prime? No: 11 × 13 math-number-theory Is 221 prime? No: 13 × 17 math-number-theory Remainder of 17 ÷ 5 2 math-number-theory 17 mod 5 2 math-number-theory Modular arithmetic Arithmetic where numbers wrap around after reaching a set value math-number-theory Clock arithmetic example 5 hours after 10 o'clock is 3 o'clock (15 mod 12) math-number-theory Even + even Even math-number-theory Odd + odd Even math-number-theory Odd + even Odd math-number-theory Odd × odd Odd math-number-theory Even × any integer Even math-number-theory Sum of the first n odd numbers n² math-number-theory Sum of the first n whole numbers n(n + 1)/2 math-number-theory Sum of 1 to 100 5,050 math-number-theory Goldbach's conjecture Every even number above 2 is the sum of two primes (unproven) math-number-theory Fermat's Last Theorem No positive integers satisfy aⁿ + bⁿ = cⁿ for n above 2; proved in 1994-95 math-number-theory Pythagorean triple Three whole numbers a, b, c with a² + b² = c² math-number-theory Common Pythagorean triples 3-4-5, 5-12-13, 8-15-17, 7-24-25 math-number-theory