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Number Theory and Roots Formula Sheet

A fuller formula sheet for primes, GCD, LCM, squares, roots, and factorials, organised around simplification and structural reasoning.

Filename: number-theory-and-roots-formula-sheet.pdfFile size: 3 KB

Formula highlights

LCM via GCD
LCM(a, b) = |a x b| / GCD(a, b)
Factorial
n! = n x (n - 1) x ... x 1

What belongs here

This pack combines the prime-factor structure behind simplification with the power and root operations that often feed geometry, algebra, and counting methods.

Formula highlights

  • Square: x^2
  • Cube: x^3
  • Nth root: value whose nth power returns the original number
  • Factorial: n! = n x (n - 1) x ... x 1

GCD and LCM reminders

  • GCD simplifies downward into shared structure.
  • LCM scales upward to a common target.
  • Prime factorisation often reveals both quickly.

Worked examples

GCD(18, 24) = 6, so 18:24 simplifies to 3:4.

LCM(6, 8) = 24 for common-denominator work.

0.81 has square root 0.9 because 0.9^2 = 0.81.

Related calculators

Use the formulas in live tools.

Guide cluster

Related reading around the same topic.