Question 36 of 36intermediate🔧 ApplyNumerical2 marks

Write two numbers whose product is 10000. The two numbers should not have 0 as the units digit.

Correct Answer

Step 1: Prime factorisation of 10000 = 2⁴ × 5⁴

Step 2: For a number not to end in 0, it should not have both 2 and 5 as factors.

Step 3: Distribute factors: Give all 2's to one number and all 5's to the other.

Step 4: First number = 2⁴ = 16, Second number = 5⁴ = 625

Step 5: 16×62516 \times 625 = 10000. Neither ends in 0.

Answer: 16 and 625

Exercise: Figure it Out (Section 6) | Q: 7 | (Page Page 20)
For More Understanding

Explanation

We need two numbers that multiply to give 10000, and neither should end in 0. Prime factorisation of 10000 = 2⁴ × 5⁴. We need to distribute these factors so neither number ends in 0 (i.e., neither has both 2 and 5 as factors). One way: 2⁴ = 16 and 5⁴ = 625. So 16×62516 \times 625 = 10000. Neither 16 nor 625 ends in 0.

Solution Steps

  1. Step 1: Prime factorisation of 10000 = 2⁴ × 5⁴

  2. Step 2: For a number not to end in 0, it should not have both 2 and 5 as factors.

  3. Step 3: Distribute factors: Give all 2's to one number and all 5's to the other.

  4. Step 4: First number = 2⁴ = 16, Second number = 5⁴ = 625

  5. Step 5: 16×62516 \times 625 = 10000. Neither ends in 0.

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