Calculating integers from their prime factor expressions | Maths

Starter quiz

Fill in the missing word: Integers greater than 1 are either composite or ______.
- 'prime' ✓
Which of the following shows that 77 is a composite number?
- 77 × 1
- 7 × 11 ✓
- 1 × 77
- 11 × 7 ✓
What is the missing number in the first step in the process to find prime factors of 75? $75 = 3 \times$ ______
- '25' ✓
What is the missing product in this process to find prime factors of 75?
- 15 + 10
- 20 + 5
- 1 × 25
- 5 × 5 ✓
Given 120 = $2^3\times3\times5$ , which of the following equals 360?
- $2^4\times3\times5$
- $2^3\times3\times5^2$
- $2^3\times3^2\times5$ ✓
Given 120 = $2^3\times3\times5$ , which of the following equals 60?
- $2^3\times3\times5$
- $2^2\times3^2\times5$
- $2^2\times3\times5$ ✓

A square number is the product of two ______ integers.
- 'repeated' ✓
Write $2^2\times3\times5$ as an integer.
- '60' ✓
True or false? $2^3\times3\times5$ is an even integer.
- True, it has a factor of 2 ✓
- False, the exponent is odd
True or false? $3\times5^2$ is a multiple of 10
- True, 5 is a factor and 10 is a multiple of 5
- False, to be a multiple of 10 it must have a factor of 2 and 5 ✓
Which of the following is not a multiple of 6?
- $2\times3^2\times5$
- $3^2\times5\times7^2$ ✓
- $2^4\times3^2\times5^2$
- $2^4\times3^2\times5$
Which of the following is a square number?
- $2\times3\times5^2$
- $2^2\times3\times5^2$
- $2^4\times3^2\times5^2$ ✓
- $2^4\times3^2\times5$

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Evaluating a product of primes will give a unique positive integer.
It is useful to compare numbers using their prime factor product without evaluating the numbers.
Square numbers can be identified from their product of primes.
Common factors can be found by comparing the products of their primes.

Identifying if integer is a multiple when its given in its prime factor form.

Only the bases need to be considered, not the exponents. e.g if it is a multiple of 3 it must be a multiple of 3^2, 3^3, etc.

Composite number - A composite number is an integer with more than two factors.
Product - A product is the result of two or more numbers multiplied together.
Prime factors - Prime factors are factors of a number that are, themselves, prime.
Exponent - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication.