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Grade 6: Equations and divisibility

10 questions with solutions for grade 6: equations, word problems, prime and composite numbers, prime factors, divisibility rules, HCF and LCM.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. Solve: x + 47 = 112Enter a number only

Solution: x = 112 − 47 = 65.

2. Solve: 8 · x = 96Enter a number only

Solution: x = 96 ÷ 8 = 12.

3. Solve: x − 39 = 61Enter a number only

Solution: x = 61 + 39 = 100.

4. A number is multiplied by 6 and then 5 is added, giving 47. What is the number?Enter a number only

Solution: 6 · x + 5 = 47, 6 · x = 42, x = 7.

5. Which number is prime?

A. 51

B. 57

C. 59

D. 91

Solution: 51 = 3 × 17, 57 = 3 × 19, 91 = 7 × 13; 59 is prime.

6. Write 84 as a product of prime factors.

A. 2 × 3 · 14

B. 2 × 2 · 3 × 7

C. 4 × 21

D. 2 × 6 · 7

Solution: 84 = 2 × 42 = 2 × 2 · 21 = 2 × 2 · 3 × 7.

7. Which number is divisible by 9?

A. 4581

B. 4582

C. 4583

D. 4586

Solution: The digit sum 4 + 5 + 8 + 1 = 18 is divisible by 9.

8. Which number is divisible by 4?

A. 7318

B. 7322

C. 7326

D. 7316

Solution: The last two digits, 16, are divisible by 4.

9. HCF(36, 48) = ?Enter a number only

Solution: 36 = 2 × 2 · 3 × 3, 48 = 2 × 2 · 2 × 2 · 3; common 2 × 2 · 3 = 12.

10. LCM(6, 8) = ?Enter a number only

Solution: Multiples of 8: 8, 16, 24…; 24 is also a multiple of 6.

Grade 6

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Natural numbers and integers
Fractions, decimals, percentages and ratio
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Circles, polygons and triangles
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