O level Maths Number Topic 1A : prime factorisation, HCF, LCM, square, cube, square root, cube root
O level Maths
Number Topic 1A : primes and prime factorisation, highest common factor, lowest common multiple, squares, cubes, square roots and cube roots solved by prime factorisation
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• primes and prime factorisation
What is a prime number?
A prime number is a number that can only be divided by itself and by 1 and cannot be divided by any other number. Prime number has exactly 2 factors only.
Prime number must be a whole number greater than 1, so the smallest prime number in the world is 2, as 2 can be divided by 2 ( itself ) and can be divided by 1 only.
Examples of prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, ...
Factors are the numbers that you need to multiply together to get another number.
Example : 6=1x6, 6=2x3, so the factors of 6 are 1,2,3 and 6.
Prime factors of a given number are the prime numbers that multiply together to produces the given number. So the prime factors of 6 is 2 and 3,
as 2 and 3 are prime numbers as well as factors.
To find prime factors of a number, use a process called continuing dividing by a prime number until the last division result is 1
Example 1: What are the prime factors of 12 ?
First, start dividing by the smallest prime number, which is 2 :
12 ÷ 2 = 6, 6 is the division result which is not 1 yet, so continue to divide by 2 again, always continue to divide by the present prime number, if not possible, then proceed to divide by the next bigger prime number. Stop dividing when the final result is 1.
So 12 = ? prime factors
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1, so stop dividing.
the divisors are 2, 2 and 3,
12 = 2x2x3 = 2x3 = prime factors in index form. Index is also known as exponent or power.
Example 2: What is the prime factors of 147 ?
147 ÷ 2 = 73½, not a whole number, so 2 is not a factor.
Let's try the next prime number, 3:
147 ÷ 3 = 49, which is a whole number, so 3 is a prime factor, continue dividing by the present prime number, if cannot divide exactly, then proceed and divide by the next prime number.
49 ÷ 3 = not a whole number, proceed to divide by the next prime number, 5.
49 ÷ 5 = also not a whole number, proceed to divide by the next prime number, 7.
49 ÷ 7 = 7 which is a whole number, so is factor.
7 ÷ 7 = 1, once the final division result is 1, stop the dividing.
So 147÷3=49
49÷7=7
7÷7=1
The divisors or prime factors of 147 are 3, 7 and 7 or 3x7x7 or 3x7.
• finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
What is the use of prime factorisation?
It helps us to find the highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots.
Example 3 : Express 216 and 400 as products of their prime factors.
Solution is in the video
Example 4 : Find the HCF of 216 and 400.
Solution is in the video
Example 5 : Find the LCM of 216 and 400
Solution is in the video
Example 6 : Find the cube and cube root of 216.
Solution is in the video
Example 7 : Find the square and positive square root of 400. Leave the answers in factor form and index form.
Solution is in the video