chap 1 (primes, HCF, LCM)

How to tell if a number is prime, composite or neither?

If a number is not a prime then it must be composite. Do you agree? Explain.

No. 1 and 0 are not prime but are not composite. As 1 only has one factor and 0 has infinite factors.

what are primes?

numbers with 2 DIFFERENT factors

what are composites?

numbers with more than 2 DIFFERENT factors

why is 23 a prime number?

It can only be divided by 1 or itself. Hence, it only has two factors and its prime.

can a product of two prime numbers be a prime number?

No. The product of two prime numbers will always have more than 2 factors.

how to determine whether a number is prime or composite?

how to present your answer when determining whether a number is prime or composite

If p and q are whole numbers such that p x q = 31, find the value of p+q. Explain your answer.

Since 31 is a prime number, then 1 and 31 are its only two factors. p + q = 1 + 31= 32

If n is a whole number such that n x (n + 28) is a prime number, find the prime number. Explain your answer.

For n x (n + 28) to be a prime number, n and n + 28 are its only two factors. Since 1 has to be one of its factors, thus n = 1. Hence, the prime number= 1 x ( 1 + 28 ) =29

Joyce uses 324 one-centimeter cubes to make a cuboid. The perimeter of the top of the cuboid is 18cm. Each side of the cuboid is longer than 2cm. Find the height of the cuboid.

• REPEATED DIVISION (324= 2x2x3x3x3x3x3)

• The length and breath of the cuboid must be a multiple of 3.

Length + Breath of the cuboid = 18 / 2

= 9

9 = 5 + 4 x

= 8 + 1 x

= 3 + 6 o

Thus, length = 6, breath = 3

Now find the height of the cuboid

OR

Since perimeter = 18 cm

2L + 2B = 18

By inspection,

2(6) + 2(3) =18

18 = 3 x 6

324 = 2x2x3x3x3x3x3

= 6(L) x 3(B) x 3(H) x3(H) x 2(H)

The height of the cuboid is 18 cm.

what is power of a perfect square and perfect cube?

perfect square= multiple of 2, perfect cube= multiple of 3

k is a non-zero whole number. Given that 15 x 135 x k is a perfect cube, write down the smallest value of k.

15 x 135 x k = 3 to the power of 4 x 5 to the power of 2 x k. x k increases the power. Hence, 3 to the power of 4 becomes 3 to the power of 6 and 5 to the power of 2 becomes 5 to the power of 3. smallest k = 3 to the power of 2 x 5 = 45

p and q are both prime numbers. Find the values of p and q so that 15 x 135 x p/q is a perfect cube. p and q must contain a factor of 3 and 5.

(p increases the power while q decreases the power). 15 x 135 x p/q = 3 to the power of 4 x 5 to the power of 2 x p/q. So, 3 to the power of 4 becomes 3 to the power of 3(decrease power) and 5 to the power of 2 becomes 5 to the power of 3 (increase power). p=5, q=3

Given that 2016/m = n to the power of 2, where m and n integers and n is as large as possible, find the value of m and n.

(n square is a perfect square) 2 to the power of 5 x 3 to the power of 2 x 7 / m. m = 2 x 7( as 2 to the power of 5 becomes 2 to the power of 4 and 7 is removed in the division) n square = 2 to the power of 4 x 3 to the power of 2. n = the square root of n square = square root of 2 to the power of 4 x 3 to the power of 2 = 2 to the power of 2 x 3 =12

Find the smallest whole number h such that 2016/h is a cube number.

how to tell if a number is a perfect square or cube from its index notation?

if the power is 2 it is a perfect square but if the power is 3 it is a perfect cube (NO MULTIPLES)

when estimating can you round up or down without rules?

yes

how to find the highest common factor of two numbers?

how to find the lowest common factor of two numbers?

The LCM of 9, 12 and k is 252. If k is odd, find all possible values of k.

The HCFof 2 numbers is 245. The LCM of these 2 numbers is 4410. Both numbers are greater than their HCF. Find these 2 numbers.

The number 240 and 252, written as the products of their prime factors, are 240 = 2 to the power of 4 x 3 x 5 and 252 = 2 to the power of 2 x 3 to the power of 2 x 7. (i) Find the smallest non-zero whole number n for which 240n is a multiple of 252. (ii) Find the smallest non-zero whole number m for which 240/m is a factor of 252.

The number 240 and 252, written as the products of their prime factors, are 240 = 2 to the power of 4 x 3 x 5 and 252 = 2 to the power of 2 x 3 to the power of 2 x 7. (ii) Find the smallest non-zero whole number m for which 240/m is a factor of 252.

how do you know whether to find the LCM or HCF of the numbers in a question?

LCM is something that continues forever while HCF has limits and does not go on forever.

What to use to estimate the square root or cube of something?

The HCF of two numbers is 175. The LCM of these two numbers is 12600. Both numbers are higher than their HCF. Find the two numbers.