Find the no of zero’s in 124!.

Sure, to find the number of zeros in 124!, we need to find the number of times 10 is a factor in the factorial. 10 is a product of 2 and 5. In any factorial, the number of 2s will always be more than the number of 5s. So, we just need to count the number of 5s in the factorial.

Here are the steps:

1. Divide 124 by 5, you get 24. This means there are 24 numbers that are multiples of 5 in the range 1 to 124.

2. But numbers like 25, 50, 75, 100, etc., are multiples of 25 (5*5), so they contribute an extra 5 to the factorial. So, divide 124 by 25, you get 4.

3. Numbers like 125 are multiples of 125 (555), so they contribute one more 5. But 124! doesn't have any multiples of 125.

So, the total number of zeros in 124! is 24 (from step 1) + 4 (from step 2) = 28.

To find the number of zeros in 124!, we need to find the number of times 10 is a factor in the factorial. Since 10 is a product of 2 and 5, we need to find the number of times 2 and 5 are factors in 124!. However, since 2 is a factor more often than 5, we only need to count the number of times 5 is a factor.

Here are the steps:

1. Divide 124 by 5. The quotient is 24. This means there are 24 numbers that are divisible by 5 in the range 1 to 124.

2. However, numbers like 25, 50, 75, 100, etc., are divisible by 5 twice. So, we need to count these extra 5s. We do this by dividing 124 by 25 (5^2). The quotient is 4.

3. We also have numbers like 125 which are divisible by 5 three times. So, we divide 124 by 125 (5^3). The quotient is 0.

4. Add up all these counts: 24 (from step 1) + 4 (from step 2) + 0 (from step 3) = 28.

So, there are 28 zeros at the end of 124!.

To find the number of zeros in 124!, we need to find the number of times 10 is a factor in the number. Since 10 is a product of 2 and 5, we need to find the number of times 2 and 5 are factors in 124!.

However, since 2 is a factor more often than 5 in any given number, we only need to find the number of times 5 is a factor in 124!.

Here's how to do it:

1. Divide 124 by 5. The result is 24.8. We only consider the whole number, so we have 24.

2. Divide 124 by 25 (5^2). The result is 4.96. We only consider the whole number, so we have 4.

3. Divide 124 by 125 (5^3). The result is 0.992. We only consider the whole number, so we have 0.

4. Add up all the whole numbers we got: 24 + 4 + 0 = 28.

So, there are 28 zeros at the end of 124!.