## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

(a) Write 90 as a product of its prime factors.

(b) Find the lowest common multiple (LCM) of 76 and 90.

## 3. | GCSE Higher |

Without using a calculator:

(a) Express 68 as the product of its prime factors.

(b) Divide 68 by 5 giving your answer in decimal format.

(c) Multiply 13.06 by 2.1

## 5. | GCSE Higher |

Show that 206 can be written as the sum of a power of five and a square number.

## 6. | GCSE Higher |

The number, \(N\), can be written as the product of prime factors in index form as:

$$N = 3 × 5^3 × x^4$$Work out \(5N^2\) as a product of prime factors in index form giving your answer in terms of \(x\).

## 7. | GCSE Higher |

Here is a list of five numbers.

$$57^{17} \quad 57^{61} \quad 57^{72} \quad 57^{83}$$(a) Find the lowest common multiple of these five numbers.

(b) Find the highest common factor of these five numbers.

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