Highest common factor | Maths | Quizalize & Oak National Academy

Starter quiz

A ______ number is the product of two repeated integers.
- 'square' ✓
Write $2^3\times3\times5^2$ as an integer.
- '600' ✓
True or false? $2^5\times3^3\times5$ is an even integer
- False, the exponents are odd
- True, it has a factor of 2 ✓
True or false? $2\times3\times5^2$ is a multiple of 10
- True, 2 and 5 are both factors ✓
- False, $5^2$ is 25 and that is not a multiple of 10
Which of the following is a multiple of 6?
- $2\times5\times7$
- $2^3\times5^2\times7$
- $2^4\times3^2\times5\times7$ ✓
- $3^2\times5\times7^3$
Which of the following is a square number?
- $2^2\times3^2\times5$
- $2^2\times3^4\times5^6$ ✓
- $2\times3^2\times5$
- $2^4\times3^2\times5^3$

The C in HCF stands for ______
- 'common' ✓
$7^5$ is a factor of an integer. Which of the following are also factors of the same integer?
- 7 ✓
- $7^8$
- $7^3$ ✓
- $7^2$ ✓
- $7^9$
Which of the following is a factor of $2^4\times3^2\times5^2$ and of $2^3\times3^4\times5$ ?
- $2^4\times3^4\times5^2$
- $2^3\times3^2\times5^2$
- $2^3\times3^2\times5$ ✓
- $2^2\times3^2\times5^2$
The HCF of 120 and 630 is ______
- '30' ✓
The HCF of 42, 60 and 90 is ______
- '6' ✓
The HCF of 36, 54 and 270 is 18. The missing prime factor in the Venn diagram is ______
- '2' ✓

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Common factors can be found by comparing the products of their primes.
The highest common factor of two numbers can be found by comparing the prime factorisation of both numbers.
Sometimes a Venn diagram can help identify the highest common factor of two numbers.
The highest common factor of more than two numbers can be found using prime factorisation.

Common factors are put into the intersection of the Venn diagram twice instead of once.

Encourage students to check that the product of the factors in each set is the correct integer.

Prime factorisation - a method to find the prime factors of a given integer
Highest common factor - The highest common factor of two or more integers  which can be divided by all other possible common factors
Hcf - an abbreviation for highest common factor