Find the number of zeroes at the end of the product of (4144 – 4143

1.	Find the number of zeroes at the end of the product of (4144 – 4143 – 4141) (5140 – 5139 – 5138).1. 1382. 2843. 4224. None of these
Answer» Correct Answer - Option 1 : 138 Given: Expression is (4¹⁴⁴ – 4¹⁴³ – 4¹⁴¹) (5¹⁴⁰ – 5¹³⁹ – 5¹³⁸) Concept used: To find the number of zeroes at the end of the product, we need to calculate the number of 2’s and number 5’s or number of pairs of 2 and 5. 2 × 5 = 10 ⇒ Number of zeroes = 1 (number of pair = 1) The number of pairs of 2 and 5 is same as the number of zeroes at the end of the product Calculation: (4¹⁴⁴ – 4¹⁴³ – 4¹⁴²) (5¹⁴⁰ – 5¹³⁹ – 5¹³⁸) ⇒ 4¹⁴² (4² – 4¹ – 4⁰) × 5¹³⁸ (5² – 5¹ – 5⁰) ⇒ 4¹⁴² (16 – 4 - 1) × 5¹³⁸ (25 – 5 - 1) ⇒ 4¹⁴² × 11 × 5¹³⁸ × 19 ⇒ (2²)¹⁴² × 11 × 5¹³⁸ × 19 ⇒ 2²⁸⁴ × 11 × 5¹³⁸ × 19 In the above expression, number of 5’s is less than the number of 2’s. So there are only 138 pairs of 2 and 5 are possible, number of zeroes would be 138 ∴ The total number of zeroes at the end of the product is 138.

Find the number of zeroes at the end of the product of (4144 – 4143 – 4141) (5140 – 5139 – 5138).1. 1382. 2843. 4224. None of these

Answer» Correct Answer - Option 1 : 138

Given:

Expression is (4¹⁴⁴ – 4¹⁴³ – 4¹⁴¹) (5¹⁴⁰ – 5¹³⁹ – 5¹³⁸)

Concept used:

To find the number of zeroes at the end of the product, we need to calculate the number of 2’s and number 5’s or number of pairs of 2 and 5.

2 × 5 = 10 ⇒ Number of zeroes = 1 (number of pair = 1)

The number of pairs of 2 and 5 is same as the number of zeroes at the end of the product

Calculation:

(4¹⁴⁴ – 4¹⁴³ – 4¹⁴²) (5¹⁴⁰ – 5¹³⁹ – 5¹³⁸)

⇒ 4¹⁴² (4² – 4¹ – 4⁰) × 5¹³⁸ (5² – 5¹ – 5⁰)

⇒ 4¹⁴² (16 – 4 - 1) × 5¹³⁸ (25 – 5 - 1)

⇒ 4¹⁴² × 11 × 5¹³⁸ × 19

⇒ (2²)¹⁴² × 11 × 5¹³⁸ × 19

⇒ 2²⁸⁴ × 11 × 5¹³⁸ × 19

In the above expression, number of 5’s is less than the number of 2’s. So there are only 138 pairs of 2 and 5 are possible, number of zeroes would be 138

∴ The total number of zeroes at the end of the product is 138.

Find the number of zeroes at the end of the product of (4144 – 4143 – 4141) (5140 – 5139 – 5138).1. 1382. 2843. 4224. None of these

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