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Primes, HCF and LCM

Secondary 1 practice

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Primes, HCF and LCM practice questions

Secondary 1 topics, the foundation the O-Level Mathematics 4052 syllabus builds on. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Is 127127 a prime number or a composite number?
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  • We test divisibility by primes up to 127=11.27(to 2 d.p.)trial division\sqrt{127} = 11.27\quad \scriptsize\text{(to 2 d.p.)}\quad \scriptsize\textit{trial division}
  • Primes to check: 2,3,5,7,112, 3, 5, 7, 11.
  • 127÷2=63.5not divisible127 \div 2 = 63.5 \quad \text{not divisible}
  • 127÷3=42.333…not divisible127 \div 3 = 42.333\ldots \quad \text{not divisible}
  • 127÷5=25.4not divisible127 \div 5 = 25.4 \quad \text{not divisible}
  • 127÷7=18.142…not divisible127 \div 7 = 18.142\ldots \quad \text{not divisible}
  • 127÷11=11.545…not divisible127 \div 11 = 11.545\ldots \quad \text{not divisible}
  • No prime factor found, so 127127 is prime.

Answer: prime

Example 2

Express 4444 as a product of its prime factors in index notation.
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  • 44÷2=22repeated division44 \div 2 = 22 \quad \scriptsize\textit{repeated division}
  • 22÷2=1122 \div 2 = 11
  • 11÷11=111 \div 11 = 1
  • 44=2×2×1144 = 2 \times 2 \times 11
  • =22×11index notation= 2^{2} \times 11 \quad \scriptsize\textit{index notation}

Answer: 22×112^2 × 11

Example 3

455455 unit cubes are arranged to form a cuboid whose three dimensions are all prime numbers. Find the dimensions of the cuboid.
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  • 455=5×7×13prime factorisation455 = 5 \times 7 \times 13 \quad \scriptsize\textit{prime factorisation}
  • The three prime factors are 55, 77, and 1313.
  • Dimensions of the cuboid: 5×7×135 \times 7 \times 13

Answer: 5,7,135,7,13

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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