TMUA Primes and Prime Factorisation
TMUA doesn't directly test primes or prime factorisation, though a few questions are easier to answer with a good knowledge of primes, prime factors and their properties. Connected to this topic is greatest common divisor (GCD), lowest common multiple (LCM) and coprime numbers, which again would not be tested directly, but certainly indirectly as part of a bigger question (note: the first four primes are 2, 3, 5 and 7 - this fact has proven useful in answering more than one TMUA question).
For those so interested, we offer both one to one TMUA coaching on primes and prime factorisation, as well as online group coaching via Zoom - 'TMUA Prerequisite Maths One' is Session #1 of 20. Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions involving primes and prime factorisation - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #162 - tests ability to calculate two numbers given their LCM and GCD - Fairly Mild
- Teaser #167 - tests how to find a multiple of various numbers using prime factors - Fairly Mild
- Teaser #423 - tests how to find the number of perfect square factors (ie products of even powers) of 162,000 - Standard
- Teaser #463 - tests how to find the number of terms in an arithmetic sequence given certain criteria (involves factors) - Standard
- Teaser #123 - tests how to solve a word problem involving products of numbers taking advantage of prime factorisation - Standard
- Teaser #406 - tests ability to split numbers into their prime factors - Standard
- Teaser #448 - tests when the fact that 143=11x13 can be used as a counterexample to statements involving primes - Medium
- Teaser #414 - tests manipulation of logs and then recognising coprime numbers - Medium
- Teaser #83 - tests how to find a person's age given almost no information (uses primes factorisation) - Medium
- Teaser #428 - tests whether '21=3x7' is a counterexample to a list of statements about primes - Medium
- Teaser #260 - tests ability to arrange fractional powers from smallest to largest using a neat trick involving LCM - Medium
- Teaser #73 - tests ability to solve a seemingly impossible word problem using prime factors - Medium
- Weekend Workout #17 - tests counting the number of ways of splitting prime factors of a number into other numbers - Medium
- Teaser #63 - tests ability to count number of integer solutions to xyz=360 - Medium
- Teaser 312 - tests how to find common terms in three different arithmetic series using LCM - Medium
- Weekend Workout #15 - tests manipulation of powers of surds according to their LCM - Medium
- Teaser #443 - tests how to find a specific number of perfect square factors of a number - Quite Tough
- Teaser #104 - tests how to find smallest integers that satisfy an equation, uses prime factorisation - Quite Tough
- Teaser #86 - tests ability to solve a crossword puzzle of sequences (including a prime one) - Quite Tough
TMUA Past Questions involving Primes and Prime Factorisation: 2016 p2 q5; 2017 p2 q5; 2017 p2 q17; 2018 p2 q7; 2018 p2 q12; 2018 p2 q17; 2019 p2 q4; 2020 p2 q4; 2021 p2 q10; 2022 p2 q3; 2023 p2 q4; 2023 p2 q11
Practice makes perfect - good luck in your studies!