Question

Express 3825 as a product of prime factors.

Answer 1

Hint: Start dividing the number with the least number you can think of and always divide it with the least only and after that write all of them in multiplication you will get the desired factors.
Complete step by step answer:
As the last digit of the number 3825 is 5 then by the rules of divisibility test we know it will be divided by 5 as it is an odd number we can't divide by 2 but we must check whether it is divisible by 3 or not before dividing with 5. We know the divisibility test for 3 is adding all the number and then see weather the added number is divisible by 3 or not if it is divisible then the whole number will be divisible
\[\therefore 3 + 8 + 2 + 5 = 18\] Now as 18 is divisible by 3 then 3825 is divisible by 3 on dividing with 3 we get it as 1275, again it is seen that it is divisible by 5 but test for 3 first
\[\therefore 1 + 2 + 7 + 5 = 15\] . As we get it as 15 then it is divisible by 3 again then we get it as 425. Now again the same thing test for 3. Since \[4 + 2 + 5 = 11\] is not divisible by 3, then we can safely divide it by 5 then we get it as 85. Since 425 does not have any factor with 3 therefore 85 will also not have so we can proceed by dividing it by 5 again and we will get it as 17. Which itself is a prime number therefore it does not have any more factors. Therefore we can write it as \[3825 = 3 \times 3 \times 5 \times 5 \times 17\] therefore 3, 5, 17 are the prime factors.

Note: Do not try to jump step, always start dividing with the lowest prime number possible it reduces the chances of making mistakes and helps to get an accurate result.