the number of zeroes at the end in the product of first 20 prime numbers
Answers
Answer: 1 zero
First three prime numbers are 2, 3 and 5. These are also included among the first 20 prime numbers.
The product of these three prime numbers end in 1 zero because of 2 × 5 = 10.
To these three prime numbers 2, 3 and 5, when we multiply other prime numbers, the no. of zero at the end of the product won't increase because there are no other prime numbers as factors of 10 except 2 and 5 to get more zero at the end of the product.
From this, we get that,
The product of first 3 or more prime numbers always end in 1 zero.
The product of first 4 prime numbers also end in 1 zero.
The product of first 5 prime numbers also end in 1 zero.
The product of first 6 prime numbers also end in 1 zero.
Thus, also, the product of first 20 prime numbers end in 1 zero.
Let's check.
2 × 3 × 5 × 7 × 11 × 13 × 17 × 19 × 23 × 29 × 31 × 37 × 41 × 43 × 47 × 53 × 59 × 61 × 67 × 71 = 557940830126698960967415390
Thus the answer is correct!