Determine the smallest positive number y such that 10500y is divisible by 11
since 11 does not divide 10500,
10500*11 = ______ is the smallest multiple of 10500 that is divisible by 11
unless you meant the six-digit number whose last digit is y.
In that case, since 105000 = 9545*11 + 5, we need to add6, giving us 105006
To determine the smallest positive number y such that 10500y is divisible by 11, we need to find the smallest value of y that makes the value of 10500y divisible by 11.
To do this, we will divide 10500 by 11 and see if the remainder is zero.
10500 ÷ 11 = 954 with a remainder of 6
Since the remainder is not zero, we need to increment y until we get a remainder of zero.
So, let's increment y by 1 and try again:
10500 × 2 = 21000
21000 ÷ 11 = 1909 with a remainder of 1
Still not zero, so let's increment y again:
10500 × 3 = 31500
31500 ÷ 11 = 2863 with a remainder of 7
Again, not zero. Let's increment y further:
10500 × 4 = 42000
42000 ÷ 11 = 3818 with a remainder of 2
Not there yet. Let's try again:
10500 × 5 = 52500
52500 ÷ 11 = 4772 with a remainder of 8
Still not zero. Let's increment y again:
10500 × 6 = 63000
63000 ÷ 11 = 5727 with a remainder of 3
Once again, not zero. Let's keep going:
10500 × 7 = 73500
73500 ÷ 11 = 6681 with a remainder of 9
No luck yet. Let's keep incrementing:
10500 × 8 = 84000
84000 ÷ 11 = 7636 with a remainder of 4
Still not zero. Let's try again:
10500 × 9 = 94500
94500 ÷ 11 = 8590 with a remainder of 0
Finally, we have found the smallest positive number y such that 10500y is divisible by 11.
Therefore, the answer is y = 9.