# Z7-I-4 stars 4949

Write instead of stars digits so the next write of product of the two numbers to be valid:
∗ ∗ ∗
· ∗ ∗ ∗
∗ ∗ ∗ ∗
4 9 4 9
∗ ∗ ∗
∗ ∗ ∗ 4 ∗ ∗

Result

a =  707
b =  176
c =  124432

#### Solution:

$4949=7 \cdot \ 7 \cdot \ 101=7^2 \cdot \ 101 \ \\ a=4949/7=707$
$b=176$
$c=a \cdot \ b=707 \cdot \ 176=124432 \ \\ s_{1}=a \cdot \ 6=707 \cdot \ 6=4242 \ \\ s_{2}=a \cdot \ 7 \cdot \ 10=707 \cdot \ 7 \cdot \ 10=49490 \ \\ s_{3}=a \cdot \ 1 \cdot \ 100=707 \cdot \ 1 \cdot \ 100=70700 \ \\ s_{4}=s_{1}+s_{2}+s_{3}=4242+49490+70700=124432$

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