Question

How moy zeroses are there at the end of the following product 1×5×10×15×20×25×30×35×40×45×50×55×60​

Answer 1

Answer:

10 Zeroes

Step-by-step explanation:

1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60​

= 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60​

Write the Equation in primary numbers

= 5 × 2×5 × 3×5 × 2×2×5 × 5×5 × 2×3×5 × 7×5 × 2×2×2×5 × 3×3×5 × 2×5×5 × 11×5 × 3×2×2×5​

Write the Equation in power of primary numbers

= 5 × 2×5 × 3×5 × 2×2×5 × 5×5 × 2×3×5 × 7×5 × 2×2×2×5 × 3×3×5 × 2×5×5 × 11×5 × 3×2×2×5​

= 5^(14) × 2^(10) × 3^(5) × 7 × 11

Now Write only 2 and 5 in the Equation

5^(14) × 2^(10)

Now Write this new Equation in 10's power

= 5^(10) × 5^(4) × 2^(10)

= 5^(10) × 2^(10) × 5^(4)

= (5×2)^(10) × 5^(4)

= 10^(10) × 5^(4)

There are 10 have power of 10

so if we solve this equation (1×5×10×15×20×25×30×35×40×45×50×55×60​)

we will get 10 Zeroes in the end of this Equations Product