the last non-zero digit in 20! is....
Answers
There are two methods you may use to find the last non-zero digit in 20! First Method The last non-zero digit in N! is same as the last non-zero digit in (N/5)!×(2^(N/5))×(N/5rem)! where N/5rem means remainder in division of N by 5. So the last non-zero digit in 20! will be same as that in (20/5)!×(2^(20/5))×(20/5rem)! =4!×2^4×0! =24×16 =384 So the last non-zero digit is 4. Second Method Notice that 9! is 362880. The last non-zero digit is 8. If we multiply 11×12×…×19, the last non-zero digit in the product must be 8 as 11,12,…,19 have the same last digits as 1,2,…,9.Multiplying by 10 and 20 give zeros as the last digit. So multipying the last digits of the two products give the last digit same as that of 8^2=64. So the last digit is 4. The process seems to be quite crude but it is easy to calcuate for large factorials using this method. For example if we take 200! we’ll get the last digit same as that of 8^20. The last digits in powers of 8 repeat as 8,4,2,6 again and again. So the last digit in 8^20 will be 6.