The numbers are \(-50,-11,9,15,27,50,83\).

(a(i)) From the list, write down a prime number. [1]

(a(ii)) Write down a cube number. [1]

(a(iii)) Write down two numbers with a product of 550. [1]

Rishwan writes each number on a card, picks a card at random and replaces it.

(b(i)) Find the probability that he picks a natural number. [1]

(b(ii)) He repeats this 140 times. Find the expected number of times he picks a natural number. [1]

(a) Given \(24192=2^7\times3^3\times7\) and \(245000=2^3\times5^4\times7^2\), find their highest common factor. [1]

(b) \(k=2^3\times3^4\times5\times c^2\), where \(c\) is a prime greater than 5. Express \(20k^2\) as a product of prime factors, in its simplest form. [2]

(a) Write 63 as a product of prime factors. [2]

(b) Find the lowest common multiple of 63 and 42. [2]

(c) Find the highest common factor of \(63a^5c^2\) and \(42a^2c^5\). [2]

A red light flashes every 20 minutes, and a blue light every 35 minutes. Both flash at 10:00. Find the next time they flash together. [3]

The list is \(\frac1{11},\ 1,\ \sqrt{41},\ 51,\ 61,\ \sqrt{81},\ 91\).

Choose from the list: (i) a cube number, (ii) a prime number, (iii) an irrational number. [3]

Give a factor of 28 that is prime. [1]

Find the highest common factor of 36 and 54. [2]

Find the LCM of \(15xy^3\) and \(18x^4y\). [2]

(a) Write 42 as a product of prime factors. [2]

(b) Find the HCF of 84 and 70. [2]

The list is \(\frac25,\sqrt{15},23,\sqrt{144},-2,0.8\).

(a) Write down a natural number from the list. [1]

(b) Write down an irrational number from the list. [1]

Find all common factors of 8 and 12. [1]

Find the largest odd common factor of 90 and 120. [1]

\(M=2^7\times3^3\times5^2\).

(a) Write 14M as a product of prime factors in index form. [2]

(b) R is an integer and M/R is a cube number. Find the smallest possible R. [2]

(a) The primes below 10 sum to 17. Find the sum of primes below 16. [2]

(b) x is an integer. The primes greater than 6 and less than x sum to 18. Give a possible x. [1]

Find the HCF of \(28x^5\) and \(98x^3\). [2]

Find the greatest odd number that is a factor of both 140 and 210. [2]

Choose from \(0.25,3.142,\sqrt3,-3,24,-0.4,1.2,-\frac14\).

Write down a natural number, an irrational number and the reciprocal of 4. [3]

From 61,62,63,64,65,66,67,68,69, write down:

(a) a cube number; [1]

(b) a prime number. [1]

Find the highest common factor of \(12x^{12}\) and \(16x^{16}\). [2]

\(12,\ 15,\ 27,\ 29,\ 91,\ 93\)

(a) From the list, write down a cube number. [1]

(b) From the list, write down a prime number. [1]

\(27,47,57,61,75,93\).

There are two prime numbers in the list. Find their sum. [2]

Find the HCF of 140 and 126. [2]

Find the LCM of \(12x^8\) and \(8x^{12}\). [2]

(a) Explain why 111 is not prime. [1]

(b) Find a prime between 110 and 120. [1]

Write 90 as a product of prime factors. [2]

From \(61,63,64,66,68,69\), write

(a) a cube number. [1]

(b) a prime number. [1]

Find the HCF of 48 and 80. [2]

Write a prime number between 30 and 40. [1]

Write 180 as a product of prime factors. [2]

\(f\) is a common factor of 14 and 28; \(m\) a common multiple of 10 and 25; \(p\) a prime. Find the largest possible value of \(f/(mp)\). [4]

Write a common multiple of 18 and 24. [1]

Find the LCM of 36 and 60. [2]

\(x=3^2\times5^2\times7\times199^{57}\) in prime factors. Write \(x\div315\) in prime factors. [2]

Numbers: \(120,121,149,164,216\).

(a) Write a square number from the list. [1]

(b) Write a cube number from the list. [1]

Find the HCF of 36 and 84. [2]

(a) Find the reciprocal of 0.2 and a prime number between 90 and 100. [2]

(b) Select an irrational number from \(7/5,\ .6,\ \sqrt7,\ 8,\ \sqrt9\). [1]

12, 18, 29, 49, 91, 125

(a) Select a cube number. [1]

(b) Select a prime number. [1]

P is a prime number with \(60<P<80\). P is 2 less than a square number. Find P. [2]

From 11, 13, 15, 17, 19, choose the number that is both prime and a factor of 195. [1]

From the list \(3.56,\quad5,\quad\sqrt{196},\quad8,\quad\sqrt7,\quad12\), write down a number that is

(a) a multiple of 3. [1]

(b) a cube number. [1]

(c) a prime number. [1]

(d) an irrational number. [1]

Find the largest odd number that is a factor of both 60 and 90. [1]

\(234=2\times3^2\times13,\quad1872=2^4\times3^2\times13,\quad234\times1872=438048\).

Write 438 048 as a product of prime factors. [1]

(a) Give a square number greater than 10. [1]

(b) Give an irrational number. [1]

From 32, 33, 34, 35, 36, 37, 38, 39, give

(a) a multiple of 8. [1]

(b) a square number. [1]

(c) a prime number. [1]

(a) 1,2,3,5,7 are common factors of two numbers. State the digit both numbers must end in. [1]

(b) Express84 as a product of primes. [2]

State the cube number greater than50 and less than100. [1]

Given \(N=2^4\times3\times7^5\), find the smallest positive integer P for which PN is a square number. [2]

The numbers are 27, 28, 29, 30, 31, 32, 33.

(a) Write down a multiple of 7. [1]

(b) Write down a cube number. [1]

(c) Write down a prime number. [1]

Write down a prime number between 50 and 60. [1]

Find the highest common factor of 90 and 48. [2]

The numbers are \(21,\ \frac23,\ \sqrt{13},\ 31,\ \sqrt{121},\ 51,\ 0.7\).

(a) Write down a prime number from the list. [1]

(b) Write down an irrational number from the list. [1]

From 87, 77, 57, 47, 27, write down

(a) a cube number. [1]

(b) a prime number. [1]

Find the HCF of 84 and 105. [2]

Write a prime number between 20 and 30. [1]

22, 17, 25, 41, 39, 4

Find the difference between the two prime numbers in this list. [2]

Complete the factors of 36: 1, 2, ____, 36. [2]

(a) Write 56 as a product of prime factors. [2]

(b) Find the LCM of 56 and 42. [2]

Find the lowest common multiple of 20 and 24. [2]

The list is \(\sqrt5,\ -7,\ 343,\ -11,\ 0.4,\ 2.5,\ \frac13\).

(a) Write a cube number. [1]

(b) Write the smallest number. [1]

(c) Write a natural number. [1]

(a) 1 and 12 are factors of 12. List all the other factors. [1]

(b) List the multiples of 9 between 20 and 40. [1]

(a(i)) Write 180 as a product of prime factors. [2]

(a(ii)) Find LCM(180,54). [2]

X,Y are integers expressed in prime factors as \(X=a^2\times7^{b+2},\quad Y=a^3\times7^2\). Their HCF is 1225 and LCM 42875.

(b) Find X,Y. [4]

(a) Write 2016 as a product of prime factors. [3]

(b) Write 2016 in standard form. [1]

Find the lowest common multiple of 36 and 48. [2]

Find the cube root of 4913. [1]

The list is \(8,9,10,11,12,13,14,15,16\). From this list, write down:

(a) the square numbers; [1]

(b) a prime factor of 99. [1]

Find the highest common factor of 56 and 70. [2]

Find the lowest common multiple of 24 and 32. [2]

(a) Write 30 as a product of prime factors. [2]

(b) Find the LCM of 30 and 45. [2]

Find the HCF of 36 and 90. [2]

From 11, 12, 13, 14, 15, 16, write down:

(a) the factors of 60; [1]

(b) the primes. [1]

(a) Write 90 as a product of prime factors. [2]

(b) Find the LCM of 90 and 105. [2]

The sum of prime numbers less than 8 is 17.

(a) Find the sum of primes less than 21. [2]

(b) The sum of primes less than x is 58. Give an integer x. [2]

Which numbers are irrational? \(\frac23,\ \sqrt{36},\ \sqrt3+\sqrt6,\ \pi,\ 0.75,\ 48\%,\ 8^{1/3}\). [2]

210, 211, 212, 213, 214, 215, 216

(a) Choose a prime number. [1]

(b) Choose a cube number. [1]

p is the largest prime between 50 and 100, and q the smallest. Find p−q. [2]