Factors and Multipliers
Find the HCF of 36 and 54
18
Write 60 as a product of prime factors
2x2x3x5
If 64=26, then find 27
128
Identify all square numbers: 4, 100, -49, 36, 150, -25.
Square numbers must be non-negative integers resulting from an integer multiplied by itself: 4, 100, 36
Calculate -4 \times -7.
28
Find the LCM of 8 and 12
24
Write 180 as a product of prime factors
2x2x3x3x5
If 64 = 43 and 4096 = 46, write 64 x 4096 in index form.
43 x 46 = 4{3+6} 49
Show that 27 is a cube number.
3 x 3 x 3 = 27 (or 33 = 27), so 27 is 3 cubed.
Calculate -45 \ 5.
-9
Use the prime factors of 180 and 315 to find their HCF
45
What are the prime factors of 60
2, 3, 5
If 64 = 43 and 4096 = 46, write 4096 \ 64 in index form.
46 \ 43 = 4{6-3} =43
Show that 50 is not a cube number.
33 = 27 and 43 = 64. Since 50 lies between 27 and 64, there is no whole number that cubes to 50.
Calculate -3 x (2 + -10).
24
Use the prime factors of 180 and 315 to find their LCM
1260
Explain why prime factorisation hels find HFC and LCM
breaks down numbers into basic building blocks
Explain the rule for multiplying powers with the same base.
Keep the base the same and add the indices/exponents (am x an = a{m+n}).
Find all possible values of n if n2 = 49.
n = 7 or n = -7
Create a negative number calculation with answer 24.
Example: -6 x -4 = 24 or -48 \ -2 = 24
Find two numbers with HCF 18 and LCM 108
18 and 108 or 36 and 54
Prime factorise 360
2x2x2x3x3x5
Simplify (23x25) \24
24
Find the value of n if n3 = -8.
n = -2 (since (-2) x (-2) x (-2) = -8)
Create and solve a negative number expression involving brackets.
Example: -2 x (5 - 9) = -2 x (-4) =8