the prime factorisation of a natural number is 2 cube×3square×5square×7.How many consecutive zeroes will it have at the end of it? Justify your answer.
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Answer: 2
Step-by-step explanation: Without the complete calculation, we can notice that our number consists of two 2s and two 5s. We require one 2 and one 5 for a 10, resulting in a zero added at the back. Hence with two 2s and two 5s, we will have two zeroes.
The third 2 will not matter, since we do not have a 5 to pair it with.
Second method, we can multiply the prime factors to check.
2³×3²×5²×7 = 12600
Hence, there are 2 zeroes at the end.
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