What is the remainder when 2006 x 2005 x 2004 x 2003 is divided by 7?

Answer 1

The trick is that:

The remainder of the product is equal to (the remainder of) the product of the remainders.

2006 / 7 = something, and remainder 4.

The remainders of 2006, 2005, 2004, 2003 are 4, 3, 2, 1.

4 x 3 x 2 x 1 = 24, when divided by 7 leaves remainder 3.

This is called "modular arithmetic" and was first worked out properly by the great Carl Friedrich Gauss (1777 - 1855).

Answer 2

2006 x 2005 x 2004 x 2003 /7
when 2006 divided by 7 remainder = 4
when 2005 divided by 7 remainder = 3
when 2004 divided by 7 remainder = 2
when 2003 divided by 7 remainder = 1
Total remainder = 4 × 3 × 2 × 1 = 24
when 24 divided by 7 remainder is 3
So answer for above = 3

Answer 3

3

Answer 4

The reminder of 1001 when is divided by 7 is zero.
(1001=7*11*13).
2003=2*1001+1
2004=2*1001+2
2005=2*1001+3
2006=2*1001+4
so the reminder is the reminder of (1*2*3*4)/7or the reminder of 24/7. Finally the reminder is 3

Answer 5

2006 x 2005 x 2004 x 2003 = 16,144,476,684,360

16,144,476,684,360 / 7 = 2,306,353,812,051.4

Answer 6

2002 = 286*7
Let 2002 = 7x

(7x+4)(7x+3)(7x+2)(7x+1)
= 7y + 4*3*2*1
= 7y + 24
= 7y + 7*3 + 3
= 7(y+3) + 3

The remainder is 3