Find the last digit of the product 723 × 813.
Correct Answer: Option B
To calculate the last digit of the product 723 × 813 we need to find the last digit for 723 and 813 individually and then multiply those last digits to get the last digit of the overall product.
Step 1: Calculate the last digit of 723
For a number of the form xy we represent the number y in the form of y = 4q + r (Where r is the remainder and q is the quotient when the number y is divided by 4). The unit digit of xy is the same as the units digit of xr.
The remainder when 23 is divided by 4 is 3.
∴ The units digit of 723 is the same as units digit of 73.
73 = 343. The unit digit is 3.
Similarly, for 813 the remainder when 13 is divided by 4 is 1.
∴ The units digit of 813 is the same as units digit of 81.
81= 8. The unit digit is 8.
∴ The last digit of 723 × 813 is the unit digit of the product of 3 and 8 = 24.
∴ The last digit of 723 × 813 = 4
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