HCF, LCM, and Prime Factors

Question 1

Find the Highest Common Factor (HCF) of 24 and 32.

Answer 1

Work out common factor pairs for each.
24: 1 24, 2 12, 3 8, 4 6.
32: 1 32, 2 16, 4 8.
So the Highest Common Factor is 8.

Question 2

Find the LCM of 8 and 12.

Answer 2

First list the multiples, then find the lowest common one.
8, 16, 24, 32.
12, 24, 36.
So LCM is 24.

Question 3

List the Prime Factors of 120.

Answer 3

First, find the lowest Prime Factor (PF). In this case it is 2. reminder 60. next PF is also 2 with remainder 30. Next is 2 reminder 15 Finally 15 is 3 x 5. So the Prime Factors of 120 are 2x2x2x3x5.

Question 4

List the first 6 Prime Numbers

Answer 4

Note that 1 is not a Prime Number.
The first 6 Prime Numbers are 2, 3, 5, 7, 11, 13.

Question 5

What are factors of a number?

Answer 5

Factors are the numbers that we multiply to get the original number.

Question 6

What is the HCF of 10 and 15?

Answer 6

5

Question 7

Find the Prime Factors of 84.

Answer 7

First prime number is 2 leaving a remainder of 42, second is also 2 with remainder 21, then it is 3 x 7. So the Prime Factors of 84 is 2 x 2 x 3 x 7.

Question 8

Find the HCF of 35 and 45.

Answer 8

Factors of 35: 1 35, 5 7.
Factors of 45: 1 45, 3 15, and 5 9.
The HCF is 5.

Question 9

Calculate the Prime Factors of 42.

Answer 9

2 x 3 x 7

Question 10

What are multiples?

Answer 10

Multiples are the results that we get from multiplying the original number by 1, 2, 3, etc.

Question 11

Work out the Lowest Common Multiple of 3 and 7.

Answer 11

First write out the multiples then find the lowest common one.
3 6 9 12 15 18 21 24
7 14 21 28
Now we ca see that the LCM is 21.