Question

Find the remainder when 101*102*103*104*105*106*107 divided by 5040

Answer 1

Answer:

The remainder will be 0

Step-by-step explanation:

5040 is having 7 factors that are 7*5*3*6*4*2.  The 105 is divisible by 7*5*3, the 102 is divisible by 6, 104 is divisible by 4, the 106 is divisible by 2.  So as the denominator became 1 and numerator is still a whole number there for it is perfectly divisible so there will be no any remainders.

Answer 2

Given:

Dividend = 101*102*103*104*105*106*107.

Divisor = 5040.

To Find:

The remainder.

Solution:

= 101*102*103*104*105*106*107 / 5040.

101*102*103*104*105*106*107 = 1.31422902E14.

So,

= 1.31422902E14 / 5040.

= 26,075,972,546.

Since, the quotient is 26,075,972,546, a whole number.

Therefore, the remainder is 0.

Hence, the remainder of the given question is 0.