Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.

[math_celebrity]

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x.

Use the quotient remainder theorem
A = B * Q + R where 0 ≤ R < B where R is the remainder when you divide A by B

Plugging in our numbers for Equation 1 we have:

• A = x
• B = 7
• Q = q
• R = 6
• x = 7 * q + 6

Plugging in our numbers for Equation 2 we have:

• A = x
• B = 11
• Q = q
• R = 2
• x = 11 * q + 2

Set both x values equal to each other:
7q + 6 = 11q + 2

Using our equation calculator, we get:
q = 1

Plug q = 1 into the first quotient remainder theorem equation, and we get:
x = 7(1) + 6
x = 7 + 6
x = 13

Plug q = 1 into the second quotient remainder theorem equation, and we get:
x = 11(1) + 2
x = 11 + 2
x = 13