Question 16 of 36intermediate🔧 ApplyNumerical2 marks

Find seven consecutive composite numbers between 1 and 100.

Correct Answer

Step 1: Look for consecutive composite numbers. Step 2: Check 90: 90 = 2×452 \times 45 (composite) Step 3: Check 91: 91 = 7×137 \times 13 (composite) Step 4: Check 92: 92 = 2×462 \times 46 (composite) Step 5: Check 93: 93 = 3×313 \times 31 (composite) Step 6: Check 94: 94 = 2×472 \times 47 (composite) Step 7: Check 95: 95 = 5×195 \times 19 (composite) Step 8: Check 96: 96 = 2×482 \times 48 (composite)

Answer: Seven consecutive composite numbers between 1 and 100 are: 90, 91, 92, 93, 94, 95, 96.

Exercise: Figure it Out (Section 3) | Q: 7 | (Page Page 8)
For More Understanding

Explanation

We need to find a sequence of 7 consecutive composite numbers. Looking at numbers after 89 (which is prime): 90=2×452 \times 45, 91=7×137 \times 13, 92=2×462 \times 46, 93=3×313 \times 31, 94=2×472 \times 47, 95=5×195 \times 19, 96=2×482 \times 48. All are composite. Another sequence: 24, 25, 26, 27, 28, 24+6=30... checking 84, 85, 86, 87, 88, 89, 90 - but 89 is prime. The sequence 90-96 works.

Solution Steps

  1. Step 1: Look for consecutive composite numbers.

  2. Step 2: Check 90: 90 = 2×452 \times 45 (composite)

  3. Step 3: Check 91: 91 = 7×137 \times 13 (composite)

  4. Step 4: Check 92: 92 = 2×462 \times 46 (composite)

  5. Step 5: Check 93: 93 = 3×313 \times 31 (composite)

  6. Step 6: Check 94: 94 = 2×472 \times 47 (composite)

  7. Step 7: Check 95: 95 = 5×195 \times 19 (composite)

  8. Step 8: Check 96: 96 = 2×482 \times 48 (composite)

  9. Step 9: 90, 91, 92, 93, 94, 95, 96 are seven consecutive composite numbers.

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