Numbers
1 389 150 = 2 x 3 x 3 x 3 x 3 x 5 x 5 x 7 x 7 x 7
Express this in index notation.
1 389 150 = 2times3^4times5^2times7^3
Which of the following are square numbers?
1, 4, 8, 10, 15, 16, 20, 27, 36, 64
1, 4, 16, 36, 64
Find the square root of the number, leaving your answer in index notation:
3^4times5^2times11^6
3^2times5times11^3
Find the highest common factor of 300 and 420.
HCF = 22 x 3 x 5 = 60
Express 504 as a product of prime factors giving your answer in index notation.
504 = 23 x 32 x 7
1, 4, 8, 9, 16, 27, 36, 64, 81, 125
4, 9, 16, 36, 81
Use prime factorisation to calculate
sqrt 2025
2025 = 3^4 times 5^2
sqrt2025= 3^2times5 = 45
Find the lowest common multiple of 300 and 420.
Leave your answer in index notation.
LCM = 22 x 3 x 52 x 7
Use prime factorisation to divide 504 by 84.
504 = 23 x 32 x 7
84 = 22 x 3 x 7
504/84 = (2^3times 3^2 times 7)/(2^2 times3 times 7)=2 times 3 = 6
What is the smallest integer that can be multiplied by 84 to form a square number?
84 = 22 x 3 x 7
Smallest integer = 3 x 7 =21
Use prime factorisation to find
root(3)(2744)
root(3)(2744) = root(3)(2^3 times 7^3) = 2times7 = 14
All the marbles need to be equally divided into identical bags which contain all three coloured marbles.
What is the largest possible number of bags that can be prepared?
HCF = 23 = 8
The largest possible number of bags is 8.