I found this theorem while going through a book:
The remainder is the same for all the multiples of the divisor and to the specific factors of the divisor that are bigger than the remainder.
Examples given:
case 1:the remainder when 1057 divided by 1000 is 57
case 2:the remainder when 1057 divided by 10000 (which is multiple of 1000) is also 57
case 3:the remainder when 1057 divided by 1000n where n is any natural number will be 57
case 1:But as per the theorem remainder when 1057 divided by 10 (which is a factor of 1000 and which is less than 57) is not 57
Can someone validate this theorem.
The remainder is the same for all the multiples of the divisor and to the specific factors of the divisor that are bigger than the remainder.
Examples given:
case 1:the remainder when 1057 divided by 1000 is 57
case 2:the remainder when 1057 divided by 10000 (which is multiple of 1000) is also 57
case 3:the remainder when 1057 divided by 1000n where n is any natural number will be 57
case 1:But as per the theorem remainder when 1057 divided by 10 (which is a factor of 1000 and which is less than 57) is not 57
Can someone validate this theorem.
