Use Euclid's division method to find the HCF of 1517 and 902.

Step 1. $1517 = 902 \times 1 + 615$.

Step 2. $902 = 615 \times 1 + 287$.

Step 3. $615 = 287 \times 2 + 41$.

Step 4. $287 = 41 \times 7 + 0$. The last divisor is $41$.

Step 5. Check. $1517 = 41 \times 37$ and $902 = 41 \times 22$, and $37$ and $22$ have no common factor.