WEBVTT 00:00:00.500 --> 00:00:03.868 Welcome to GCSE Edexcel Maths revision. 00:00:04.018 --> 00:00:07.214 Topic M 2: Factors, multiples and primes. 00:00:07.364 --> 00:00:09.540 This video covers Higher tier. 00:00:09.690 --> 00:00:13.680 It includes the shared content and the labelled Higher extensions. 00:00:16.333 --> 00:00:21.889 A factor divides a number exactly; a multiple is made by multiplying it by an integer. 00:00:22.039 --> 00:00:30.636 The positive factors of 12 are 1, 2, 3, 4, 6 and 12; its positive multiples start 12, 24, 36, and so on. 00:00:33.300 --> 00:00:37.039 A prime has exactly two positive factors, 1 and itself. 00:00:37.189 --> 00:00:40.891 The first primes are 2, 3, 5, 7, 11, 13. 00:00:41.041 --> 00:00:44.505 The number 1 is not prime and 2 is the only even prime. 00:00:47.167 --> 00:01:00.434 Use divisibility tests to find factors: an even number is divisible by 2; a digit sum divisible by 3 indicates divisibility by 3; a final digit 0 or 5 indicates divisibility by 5. 00:01:03.100 --> 00:01:07.913 Prime factorisation writes a whole number greater than 1 as a product of primes. 00:01:08.063 --> 00:01:14.740 A factor tree or repeated division gives 60 equals 2 squared multiplied by 3 multiplied by 5. 00:01:14.890 --> 00:01:17.279 The product is unique apart from order. 00:01:17.429 --> 00:01:19.520 Prime factor tree for 60 00:01:24.200 --> 00:01:31.303 The highest common factor open bracket H C F close bracket is the largest factor shared by two or more numbers. 00:01:31.453 --> 00:01:36.497 In prime factorisations, take only common primes with the smallest shared powers. 00:01:39.167 --> 00:01:46.525 The lowest common multiple open bracket L C M close bracket is the smallest positive multiple shared by the numbers. 00:01:46.675 --> 00:01:50.212 Take every prime that appears, with the largest power needed. 00:01:52.867 --> 00:02:02.796 Worked example: 36 equals 2 squared multiplied by 3 squared and 48 equals 2 to the power of open bracket 4 close bracket multiplied by 3. 00:02:02.946 --> 00:02:14.699 H C F equals 2 squared multiplied by 3 equals 12; L C M equals 2 to the power of open bracket 4 close bracket multiplied by 3 squared equals 144. 00:02:17.367 --> 00:02:26.345 H C F helps divide quantities into identical largest-sized groups: 36 red and 48 blue counters make 12 identical groups, 00:02:26.495 --> 00:02:29.375 each containing 3 red and 4 blue counters, 00:02:29.525 --> 00:02:31.083 with none left over. 00:02:33.733 --> 00:02:36.783 L C M helps find when cycles coincide. 00:02:36.933 --> 00:02:43.747 Alarms ringing every 6 and 8 minutes next ring together after 24 minutes, provided they ring together initially. 00:02:46.400 --> 00:02:50.401 List outcomes systematically so none are missed or counted twice. 00:02:50.551 --> 00:02:58.689 With digits 1, 2 and 3 and no repetition, two-digit numbers are 12, 13, 21, 23, 31 and 32. 00:03:01.367 --> 00:03:05.263 If order does not matter, A B and B A represent the same pair. 00:03:05.413 --> 00:03:09.829 State whether repetitions are allowed and whether order matters before counting. 00:03:12.500 --> 00:03:19.346 If there are m choices for one stage and n choices for the next stage for every first choice, there are m n outcomes. 00:03:19.496 --> 00:03:24.447 Three shirts and four trousers give 3 multiplied by 4 equals 12 outfits. 00:03:27.100 --> 00:03:32.945 Worked example: A code uses two different letters from A to E followed by a digit 0 to 9. 00:03:33.095 --> 00:03:37.773 There are 5 multiplied by 4 multiplied by 10 equals 200 codes. 00:03:37.923 --> 00:03:42.214 The second letter has only four choices because repetition is forbidden. 00:03:44.867 --> 00:03:49.511 For restrictions, split into separate cases or subtract forbidden outcomes. 00:03:49.661 --> 00:03:56.326 The product rule needs the correct number of choices at every stage; choices need not be statistically independent. 00:03:59.000 --> 00:04:01.805 That completes Factors, multiples and primes. 00:04:01.955 --> 00:04:05.300 Revisit the notes and test yourself on the revision website.