Using Venn diagrams

A Venn diagram shows the relationship between different sets or categories of data.

For example, the following list of numbers can be sorted depending on whether the numbers are even or not, and whether or not they are multiples of 3.

1, 3, 4, 5, 6, 8, 9, 14, 18

A venn diagram with even numbers on the left, multiples of 3 on the right and both even numbers and multiples of three in the middle.

The numbers 1 and 5 are neither even nor multiples of 3, so they are placed outside the rings of the Venn diagram. The numbers 6 and 18 are multiples of 3 that are also even numbers, so they are placed in the overlap (or intersection) of the two rings.

Venn diagrams can be used to calculate the highest common factors (HCFs) and lowest common multiples (LCMs) of numbers.

Example

Find the HCF and LCM of 24 and 180.

Break the numbers into the product of prime factors using prime factor trees, as before.

The product of prime factors for 24 are: 2 \times 2 \times 2 \times 3

The product of prime factors for 180 are: 2 \times 2 \times 3 \times 3 \times 5

Put each prime factor in the correct place in the Venn diagram. Any common factors should be placed in the intersection of the two circles.

A venn diagram showing the prime factors of 24 and the prime factors of 180.

The highest common factor is found by multiplying together the numbers in the intersection of the two circles.

HCF = 2 \times 2 \times 3 = 12

The LCM is found by multiplying together the numbers from all three sections of the circles.

LCM = 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 360

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