IGCSE›Edexcel IGCSE Maths›Mind mapsPrime Factors, HCF & LCMEdexcel IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsPrime factorsEvery integer above 1 has a unique prime factorisationDivide repeatedly by the smallest prime until you reach 1360=23×32×5360 = 2^{3} \times 3^{2} \times 5360=23×32×5A factor tree splits until every end is primeFinding HCFHCF is the largest number dividing into bothWrite each number as a product of primesTake the lowest power of each shared primeHCF of 360 and 252: 22×32=362^{2} \times 3^{2} = 3622×32=36Finding LCMLCM is the smallest number both divide intoTake the highest power of every prime in either listLCM of 360 and 252: 23×32×5×7=25202^{3} \times 3^{2} \times 5 \times 7 = 252023×32×5×7=2520HCF & LCMprime factorsHCFLCMThe linkHCF×LCM=a×b\text{HCF} \times \text{LCM} = a \times bHCF×LCM=a×bCheck: 36×2520=360×252=90,72036 \times 2520 = 360 \times 252 = 90{,}72036×2520=360×252=90,720HCF keeps what is common; LCM covers everythingWord problemsLargest equal groups or sharing with none left: HCFBuses leaving together again: LCMBus example: every 12 and 18 minutes gives LCM 36Exam tipsWrite answers in index notation, not repeated primesKeep dividing until every branch is prime, not 4 or 9A prime is its own only prime factor: 7=717 = 7^{1}7=71