Question

How many zeros are there at the end of 200 factorial?​

Answer 1

Answer:

Since there are 49 factors of 5 within 200!, there are 49 5-and-2 pairs and thus 49 trailing zeros.

Answer 2

Solution :-

Concept :-

• In last of a number 2 and 5 makes zeros as 2 * 5 becomes 10 .
• So, we have to check how many 2 or 5 comes in 200! .
• As we know that, 2 is a multiple of every even number , therefore, it is difficult to count total number of two's in 200! .
• Then, we can count total number of 5's in 200! .

So,

→ 200 ÷ 5 = 40 Quotient

→ 40 ÷ 5 = 8 Quotient

→ 8 ÷ 5 = 1 Quotient .

therefore,

→ Total number of 5's in 200! are = 40 + 8 + 1 = 49 .

hence, we can conclude that, total number of zeros at the end of 200! are 49 .

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