Primes, Highest Common Factor and Lowest Common Multiple Flashcards
(18 cards)
why are 0 and 1 special numbers
they are neither prime nor composite
prime number definition
it is a whole number that has exactly 2 different factors, 1 and itself
composite number definition
it is a whole number that has more than 2 different factors
write 5⁴ in index notation
5 x 5 x 5 x 5
Find √324 using prime factorisation
Use prime factors to explain why 6 x 24 is a perfect square
6 x 24 = (2 x 3) x (2³ x 3) = 2⁴ x 3²
Since the index of each prime factors of 6 x 24 is even, then 6 x 24 is a perfect square
k is a non-zero whole number. given that 6 x 24 x k is a perfect cube, write down the smallest value of k
6 x 24 x k = 2⁴ x 3² x k
For k to be the smallest, k=2² x 3 so that 2⁴ x 3² x k= 2⁴ x 3² x (2² x 3) = 2⁶ x 3³ is a perfect cube
∴ smallest value of k = 2² x 3 = 12
p and q are both prime numbers. find the values of p and q so that 6 x 24 x p/q is a perfect cube
6 x 24 x p/q = 2⁴ x 3² x p/q
p and q must contain a factor of 2 or 3
Since p and q are prime numbers, then one of them must be 2 and the other 3 (cannot be a multiple of 2 or 3)
∴ p=3 and q=2 so that 2⁴ x 3² x p/q = 2⁴ x 3² x 3/2 = 2³ x 3³ is a perfect cube
why cant use prime factorisation method to find numbers like √50
because 50=2 x 5² is not a perfect square, so √50 is not a whole number
if we cant use prime factorisation method for numbers like √50, then what can we use?
estimation
estimate the value of √50
√50 ≈ √49 = 7
Find the HCF of 40, 60 and 100 (prime factorisation or ladder method)
find the lowest common multiple of 30 and 36
A number has exactly 8 factors, 2 of which are 6 and 27. list all the factors of the number
The highest common factor of two numbers is 56
The lowest common multiple of these two numbers is 2520
Both numbers are greater than 56. Find the 2 numbers
HCF = 56 = 2³ x 7
LCM= 2520 = 2³ x 7 x 3² x 5 = (2³ x 7) x 3² x 5
Let the 2 numbers be a and b
a = 2³ x 7 x ?
b = 2³ x 7 x ?
a = 2³ x 7 x 3²
b = 2³ x 7 x 5
∴ the two numbers are 504 and 280
The lights on three lightships flash at regular intervals. The first light flashes every 18 seconds, the second every 30 seconds and the third every 40 seconds. the three lights flash together at 10:00pm. At what time will they next flash together?
18 = 2 x 3²
30 = 2 x 3 x 5
40= 2³ x 5
∴ LCM of 18, 30 and 40 = 2³ x 3² x 5 = 360
360 seconds =6 minutes
∴ the three lights will next flash together at 10:06pm
HCF definition
it is two or more numbers is the largest factor that is common to all the numbers
LCM definition
two or more numbers is the smallest multiple that is common to all the numbers
