Question

How many zeros at the end of the product 4^5×6^11

Answer 1

Answer:

There will be only one zero at the end

The answer will be 1320

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let us start solving the question by starting with when the product of numbers results in zero at the end.

If the end of a product or the unit digit of a number is zero, it means it is divisible by 10, that is it is a multiple of 10.

So, the number of zeros at the end of any number is equal to the number of times that number can be factored into the power of 10.

For example, we can write 200 as 200=2×10×10=2×(10)2200=2×10×10=2×(10)2. In it we can see that the number of zeroes is equal to the number of times 10 is raised to power.

As 10=2×510=2×5, we can say that the number of zeroes in the end is equal to the power of 5 in the product.

Now, let us consider the product .

As we need to find the number of zeros at the end of the product, we can find the number to which 5 is raised in the product as they are equal.

So, to find that we need to consider all the multiples of 5 present in the given product. They are 5, 10, 15, 20, 25, 30.

In 5656, as it is 5 itself it has 6 fives.

In 10111011, as 10=2×510=2×5, it has 11 fives.

In 15161516, as 15=3×515=3×5, it has 16 fives.

In 20212021, as 20=2×2×520=2×2×5, it has 21 fives.

In 25262526, as 25=5×525=5×5, it has 26 fives two times, that is 52 fives.

In 30313031, as 30=2×3×530=2×3×5, it has 31 fives.

As we need the total number of fives in the product, let us add all the above possible fives. Then we get,

6+11+16+21+52+31=1376+11+16+21+52+31=137

So, number of zeros at the end of the product of

So, the correct answer is 137.