Question

write the nuber of zeroes in the end of a number whose prime factorization is 2*2×5*3×3*2×17​

Answer 1

Answer:

concept : if we multiply 10 with any number, we get a zero in unit digit of resultant number.similarly when we multiply 100 with any number, we get two zeros in the end of resultant number and so on. for example ; 10 × 45 = 450.

100 × 45 = 4500.

means, for getting number of zeros in the end of a number we have to check how much multiple of 10 are present in that number.

here, given prime factorisation of number is 2² × 5³ × 3² × 17

= 2² × 5² × 5 × 3² × 17

= (2 × 5)² × 5 × 3² × 17

= (10)² × 5 × 3² × 17

= 10 × 10 × 5 × 3² × 17

here , there are two 10 are present in the prime factorisation of number so, \textbf{two zeros}two zeros are present in the end of the given number.

Answer 2

we have,

2² × 5³ × 3² × 17

2² × 5² × 5 × 3² × 17

(2 × 5)² × 5 × 3² × 17

(10)² × 5 × 3² × 17

100 × 5 × 3² × 17

Clearly, there are two zeros at the end of the given number.