This GMAT Math practice question is a number properties question covering the concept of factorials and the highest power of a prime number that can divide a factorial. A GMAT 700 level sample question.
Question 7: How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?
25! means factorial 25 whose value = 25 * 24 * 23 * 22 *....* 1
When a number that is a multiple of 5 is multiplied with an even number, it results in a trailing zero.
(Product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)
In 25!, the following numbers have 5 as their factor: 5, 10, 15, 20, and 25.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.
There are at least 6 even numbers in 25!
Hence, the number 25! will have 6 trailing zeroes in it.
Make sure you watch the explanation video embedded above for a methodical shortcut to find the number of trailing zeroes.
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5. Number Properties | Tests of divisibility
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8. GMAT Number Theory | Prime factorization | Properties of squares & cubes
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20. Number Theory | Highest power of a prime that divides factorial of 'n'
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22. Number Theory | Number of trailing zeroes in a number
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