# Use a congruence modulo 9 to find the missing digit, indicated by a question mark: 89, 878*58,965=5299? 56270.

Use a congruence modulo 9 to find the missing digit, indicated by a question mark: 89, 878*58,965=5299? 56270.
You can still ask an expert for help

## Want to know more about Congruence?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Amir Hanna
Notice that $89,878\equiv 8+9+8+7+8\equiv 4\left(mod9\right),58,965\equiv 5+8+9+6+5\equiv 6\left(mod9\right)$, and $5,299,?56,270\equiv 5+2+9+9?+5+6+2+7+0\equiv ?\left(mod9\right)$. Now, $89,878\ast 58,965\equiv 4\ast 6\equiv 6\equiv ?\left(mod9\right)$. Thus, as the question mark represents a single decimal digit, we get that ?=6
Result:
The missing digit indicated by the question mark is 6.