Question 29 of 36intermediate🔍 AnalyzeShort Answer2 marks

The first number has prime factorisation 2×32 \times 3 × 7 and the second number has prime factorisation 3×73 \times 7 × 11. Are they co-prime? Does one of them divide the other?

Correct Answer

Step 1: First number = 2×32 \times 3 × 7 = 42

Step 2: Second number = 3×73 \times 7 × 11 = 231

Step 3: Common prime factors: 3 and 7

Step 4: Since common prime factors exist, the numbers are NOT co-prime.

Step 5: For divisibility: 42 has prime factor 2 which is not in 231 ∴ 42 does not divide 231 231 has prime factor 11 which is not in 42 ∴ 231 does not divide 42

Answer: The two numbers are NOT co-prime and neither divides the other.

Exercise: Figure it Out (Section 5) | Q: 3 | (Page Page 16)
For More Understanding

Explanation

First number = 2×32 \times 3 × 7 = 42. Second number = 3×73 \times 7 × 11 = 231. Common prime factors: 3 and 7. So they are not co-prime. For divisibility: 42 has prime factor 2 which is not in 231, so 42 does not divide 231. 231 has prime factor 11 which is not in 42, so 231 does not divide 42.

Solution Steps

  1. First number = 2×32 \times 3 × 7 = 42

  2. Second number = 3×73 \times 7 × 11 = 231

  3. Common prime factors: 3 and 7

  4. Since common prime factors exist, the numbers are NOT co-prime

  5. 42 has prime factor 2 which is not in 231, so 42 does not divide 231

  6. 231 has prime factor 11 which is not in 42, so 231 does not divide 42

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