Topics › KS3 › Number

Factors, multiples & primes

fmp-01 Present from here

Which list shows all the prime numbers less than $10$?

Option A: $1,\ 3,\ 5,\ 7,\ 9$

Option B: $3,\ 5,\ 7$

Option C: $2,\ 3,\ 5,\ 7$

Option D: $1,\ 2,\ 3,\ 5,\ 7$

Answer and misconceptions

Option A: $1,\ 3,\ 5,\ 7,\ 9$ ✗
Thinks prime means oddLists the odd numbers, including 1 and 9, and leaves out 2.

Option B: $3,\ 5,\ 7$ ✗
Thinks 2 is not prime because it is evenBelieves no even number can be prime.

Option C: $2,\ 3,\ 5,\ 7$ ✓ Correct

Option D: $1,\ 2,\ 3,\ 5,\ 7$ ✗
Thinks 1 is a prime numberDoes not know a prime has exactly two factors; 1 has only one.
fmp-02 Present from here

Which list shows all the factors of $12$?

Option A: $2,\ 3,\ 4,\ 6$

Option B: $2,\ 3$

Option C: $12,\ 24,\ 36,\ 48$

Option D: $1,\ 2,\ 3,\ 4,\ 6,\ 12$

Answer and misconceptions

Option A: $2,\ 3,\ 4,\ 6$ ✗
Leaves out 1 and the number itselfThinks 1 and 12 do not count as factors of 12.

Option B: $2,\ 3$ ✗
Confuses factors with prime factorsLists only the prime numbers that divide 12.

Option C: $12,\ 24,\ 36,\ 48$ ✗
Confuses factors with multiplesLists numbers in the 12 times table instead of numbers that divide 12.

Option D: $1,\ 2,\ 3,\ 4,\ 6,\ 12$ ✓ Correct
fmp-03 Present from here

What is the highest common factor (HCF) of $12$ and $18$?

Option A: $2$

Option B: $6$

Option C: $36$

Option D: $216$

Answer and misconceptions

Option A: $2$ ✗
Gives the lowest common factor above 1Finds a common factor but stops at the smallest one.

Option B: $6$ ✓ Correct

Option C: $36$ ✗
Confuses HCF with LCMFinds the lowest common multiple instead.

Option D: $216$ ✗
Multiplies the two numbersThinks multiplying 12 x 18 combines their factors.
fmp-04 Present from here

What is the lowest common multiple (LCM) of $6$ and $8$?

Option A: $24$

Option B: $48$

Option C: $2$

Option D: $8$

Answer and misconceptions

Option A: $24$ ✓ Correct

Option B: $48$ ✗
Always multiplies the two numbers for the LCM6 x 8 is a common multiple, but not the lowest one.

Option C: $2$ ✗
Confuses LCM with HCFGives the highest common factor instead of a multiple.

Option D: $8$ ✗
Assumes the larger number is the LCMAssumes the larger number is always a multiple of the smaller.
fmp-05 Present from here

Which shows $60$ written as a product of its prime factors?

Option A: $2 \times 3 \times 5$

Option B: $2^2 \times 3 \times 5$

Option C: $4 \times 3 \times 5$

Option D: $1 \times 2^2 \times 3 \times 5$

Answer and misconceptions

Option A: $2 \times 3 \times 5$ ✗
Lists each prime factor only onceLeaves out the repeated factor of 2; 2 x 3 x 5 = 30.

Option B: $2^2 \times 3 \times 5$ ✓ Correct

Option C: $4 \times 3 \times 5$ ✗
Includes a factor that is not primeStops splitting at 4, which is not prime.

Option D: $1 \times 2^2 \times 3 \times 5$ ✗
Treats 1 as a prime factorIncludes 1, which is not prime.