Number System

Divisibility rules 2 to 13 · Unknown digits: 72, 88, 99 · Composite divisor · Consecutive products: 6, 24, 8 · Digit sum conditions · Counting multiples in range · Power sums: odd powers, add the bases · Not Necessarily Divisible · Repdigit and Block Numbers

Count of factors: one formula, two traps · Sum of Factors: One Bracket per Prime · Perfect square and cube factors · Factor Pairs: Count, Don't Double · Factors that are multiples of k · Product of All Divisors: Pair Them · Odd and Even Factors · Smallest number from its factor count · Coprimes below n: Euler's phi

Cyclicity: shrink the huge power · Negative Remainder: fix the minus sign · Binomial trick · Fermat's Little Theorem · Successive Division: Rebuild Upwards · Sum of factorials · Large power mod 9 · Dividend = divisor x quotient + remainder · Wilson's Theorem: 150! mod 151 · Concatenated number remainder · Geometric sum remainder

Unit digit: the cycle of 4 · Unit Digit of Sums and Products · Last two digits · Factorial unit digit · Reverse the Unit Digit: Cubes · Unit Digit of Power Towers

Highest power in factorial · Trailing zeros · Composite base: scarcest prime wins · Trailing Zeros: The Inverse Trick · Zeros in products

Digit Count of 2^a × 5^b · Number from digit relations · Digit sum ratio · k-th Digit of 123456789101112... · Four digit number conditions · Digit occurrence count · Recurring decimal kth digit

Two variable diophantine · Sum equals product · Bounded Integer Solutions · Min sum under linear constraint · Difference of squares pairs · Reciprocal sum equation · Lattice Points: Diamond and Circle

Primes composites · Perfect square properties · Rational irrational · Squares ending digits · Terminating Decimals: The 2-5 Test · Parity statements

BODMAS: Chained Division · Square cube roots · Fraction ordering · Operator substitution · Surd approximation · Recurring decimal fraction · Decimal to Fraction in One Move · Power Sum Identities

Decimal to base · Base to Decimal in Seconds · Binary digit numbers · Unknown base equation · Digit count in base · Last digits in base

Prime factorisation: HCF and LCM · HCF times LCM: the product rule · HCF and LCM of Fractions · HCF by Division and Difference · HCF and LCM of Decimals · Ratio and HCF, the hidden multiplier · HCF of powers minus 1 · LCM is k times HCF · LCM of the First n Numbers

Same Remainder: HCF of Differences · Remainders: LCM plus r or minus d · Bells tolling: LCM, not addition · Max Tile Size: The HCF Fits All · Co-prime pairs: product and sum · HCF and sum: find the two numbers · Least perfect square multiple · n-digit numbers divisible by a set · Count with a given gcd