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Home / Practice / Maths
Highest common factors, lowest common multiples, prime numbers and square numbers.
Question 1 of 12
What is the highest common factor of 72 and 40?
A common factor has to divide into both numbers exactly. 8 does: 72 ÷ 8 = 9 and 40 ÷ 8 = 5, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. List the factors of the smaller number first and work down from the top. The first one that also divides the larger number is the answer.
The answer is C. A common factor has to divide into both numbers exactly. 8 does: 72 ÷ 8 = 9 and 40 ÷ 8 = 5, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. List the factors of the smaller number first and work down from the top. The first one that also divides the larger number is the answer.
What is the highest common factor of 20 and 24?
A common factor has to divide into both numbers exactly. 4 does: 20 ÷ 4 = 5 and 24 ÷ 4 = 6, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. The highest common factor is never bigger than the smaller of the two numbers.
The answer is D. A common factor has to divide into both numbers exactly. 4 does: 20 ÷ 4 = 5 and 24 ÷ 4 = 6, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. The highest common factor is never bigger than the smaller of the two numbers.
What is the lowest common multiple of 8 and 6?
Counting in 8s gives 8, 16, 24, 32 and so on; counting in 6s gives 6, 12, 18, 24. The first number that appears in both lists is 24. Multiplying 8 × 6 gives 48, which is a common multiple but not the lowest one. That is the trap in this question. Multiplying the two numbers always gives a common multiple. It is just not always the lowest.
The answer is A. Counting in 8s gives 8, 16, 24, 32 and so on; counting in 6s gives 6, 12, 18, 24. The first number that appears in both lists is 24. Multiplying 8 × 6 gives 48, which is a common multiple but not the lowest one. That is the trap in this question. Multiplying the two numbers always gives a common multiple. It is just not always the lowest.
What is the highest common factor of 63 and 14?
A common factor has to divide into both numbers exactly. 7 does: 63 ÷ 7 = 9 and 14 ÷ 7 = 2, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. The highest common factor is never bigger than the smaller of the two numbers.
The answer is D. A common factor has to divide into both numbers exactly. 7 does: 63 ÷ 7 = 9 and 14 ÷ 7 = 2, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. The highest common factor is never bigger than the smaller of the two numbers.
What is the lowest common multiple of 4 and 7?
Counting in 4s gives 4, 8, 12, 16 and so on; counting in 7s gives 7, 14, 21, 28. The first number that appears in both lists is 28. Here 4 and 7 share no factors, so multiplying them gives the answer — but that shortcut only works when they share nothing. The lowest common multiple is never smaller than the larger of the two numbers.
The answer is B. Counting in 4s gives 4, 8, 12, 16 and so on; counting in 7s gives 7, 14, 21, 28. The first number that appears in both lists is 28. Here 4 and 7 share no factors, so multiplying them gives the answer — but that shortcut only works when they share nothing. The lowest common multiple is never smaller than the larger of the two numbers.
What is the highest common factor of 40 and 32?
A common factor has to divide into both numbers exactly. 8 does: 40 ÷ 8 = 5 and 32 ÷ 8 = 4, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. List the factors of the smaller number first and work down from the top. The first one that also divides the larger number is the answer.
The answer is C. A common factor has to divide into both numbers exactly. 8 does: 40 ÷ 8 = 5 and 32 ÷ 8 = 4, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. List the factors of the smaller number first and work down from the top. The first one that also divides the larger number is the answer.
What is the lowest common multiple of 10 and 6?
Counting in 10s gives 10, 20, 30, 40 and so on; counting in 6s gives 6, 12, 18, 24. The first number that appears in both lists is 30. Multiplying 10 × 6 gives 60, which is a common multiple but not the lowest one. That is the trap in this question. Count in the larger number and check each one against the smaller. It is far quicker than listing both.
The answer is B. Counting in 10s gives 10, 20, 30, 40 and so on; counting in 6s gives 6, 12, 18, 24. The first number that appears in both lists is 30. Multiplying 10 × 6 gives 60, which is a common multiple but not the lowest one. That is the trap in this question. Count in the larger number and check each one against the smaller. It is far quicker than listing both.
Which of these is a prime number?
A prime number has exactly two factors: itself and 1. 61 has no other factors — it is not even, it does not end in 0 or 5, and its digits do not add to a multiple of 3 (6 + 1 = 7). Every other option can be divided by something. Test 2, 3, 5 and 7 in that order. For any number under 100 that is enough to settle it.
The answer is B. A prime number has exactly two factors: itself and 1. 61 has no other factors — it is not even, it does not end in 0 or 5, and its digits do not add to a multiple of 3 (6 + 1 = 7). Every other option can be divided by something. Test 2, 3, 5 and 7 in that order. For any number under 100 that is enough to settle it.
What is the highest common factor of 28 and 49?
A common factor has to divide into both numbers exactly. 7 does: 28 ÷ 7 = 4 and 49 ÷ 7 = 7, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. List the factors of the smaller number first and work down from the top. The first one that also divides the larger number is the answer.
The answer is A. A common factor has to divide into both numbers exactly. 7 does: 28 ÷ 7 = 4 and 49 ÷ 7 = 7, both with nothing left over. Nothing larger works, which is what makes it the highest. Checking is worth doing on both numbers — a value that divides one of them and not the other is the usual wrong answer here. List the factors of the smaller number first and work down from the top. The first one that also divides the larger number is the answer.
Which of these is a square number?
A square number is what you get when a whole number is multiplied by itself. 9 × 9 = 81, so 81 is square. 18 would be 9 doubled, which is a different thing entirely, and 90 is 9 × 10 — close, but the two numbers have to match. Square numbers get further apart as they grow: 1, 4, 9, 16, 25, 36. The gaps are the odd numbers.
The answer is C. A square number is what you get when a whole number is multiplied by itself. 9 × 9 = 81, so 81 is square. 18 would be 9 doubled, which is a different thing entirely, and 90 is 9 × 10 — close, but the two numbers have to match. Square numbers get further apart as they grow: 1, 4, 9, 16, 25, 36. The gaps are the odd numbers.
A square number is what you get when a whole number is multiplied by itself. 4 × 4 = 16, so 16 is square. 8 would be 4 doubled, which is a different thing entirely, and 20 is 4 × 5 — close, but the two numbers have to match. Square numbers get further apart as they grow: 1, 4, 9, 16, 25, 36. The gaps are the odd numbers.
The answer is C. A square number is what you get when a whole number is multiplied by itself. 4 × 4 = 16, so 16 is square. 8 would be 4 doubled, which is a different thing entirely, and 20 is 4 × 5 — close, but the two numbers have to match. Square numbers get further apart as they grow: 1, 4, 9, 16, 25, 36. The gaps are the odd numbers.
What is the lowest common multiple of 6 and 15?
Counting in 6s gives 6, 12, 18, 24 and so on; counting in 15s gives 15, 30, 45, 60. The first number that appears in both lists is 30. Multiplying 6 × 15 gives 90, which is a common multiple but not the lowest one. That is the trap in this question. Multiplying the two numbers always gives a common multiple. It is just not always the lowest.
The answer is D. Counting in 6s gives 6, 12, 18, 24 and so on; counting in 15s gives 15, 30, 45, 60. The first number that appears in both lists is 30. Multiplying 6 × 15 gives 90, which is a common multiple but not the lowest one. That is the trap in this question. Multiplying the two numbers always gives a common multiple. It is just not always the lowest.
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