Question 6 of 36intermediate🔧 ApplyNumerical2 marks

A number for which the sum of all its factors is equal to twice the number is called a perfect number. The number 28 is a perfect number. Its factors are 1, 2, 4, 7, 14 and 28. Their sum is 56 which is twice 28. Find a perfect number between 1 and 10.

Correct Answer

Definition: A perfect number has the sum of all its factors equal to twice the number.

Step 1: Check each number from 1 to 10.

Step 2: For 6, factors are 1, 2, 3, 6.

Step 3: Sum of factors = 1 + 2 + 3 + 6 = 12.

Step 4: Twice the number = 2×62 \times 6 = 12.

Step 5: Since sum of factors equals twice the number, 6 is a perfect number.

Answer: The perfect number between 1 and 10 is 6.

Exercise: Figure it Out (Section 2) | Q: 3 | (Page Page 5)
For More Understanding

Explanation

A perfect number has the sum of all its factors equal to twice the number. Checking numbers from 1 to 10: For 6, factors are 1, 2, 3, 6. Sum = 1 + 2 + 3 + 6 = 12 = 2×62 \times 6. Therefore, 6 is a perfect number.

Solution Steps

  1. Step 1: Check each number from 1 to 10.

  2. Step 2: For 6, factors are 1, 2, 3, 6.

  3. Step 3: Sum of factors = 1 + 2 + 3 + 6 = 12.

  4. Step 4: Twice the number = 2×62 \times 6 = 12.

  5. Step 5: Since sum of factors equals twice the number, 6 is a perfect number.

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