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Problem 3

# Find the quotient $$\mathrm{q}$$ and remainder $$\mathrm{r}$$ upon dividing 575 by 21 .

Expert verified
Upon dividing 575 by 21, we find that the quotient $$q = 27$$ and remainder $$r = 8$$.
See the step by step solution

## Step 1: Setting up the long division problem

Write the division problem as a long division. In this case, we will be dividing 575 (dividend) by 21 (divisor). So, write 575 under the division bracket and 21 on the left side of the bracket.

## Step 2: Perform the division

Now, we will perform the long division by trying to find how many times the divisor (21) can fit into each part of the dividend (575) till we can no longer divide.

## Step 3: Division with the first part

Find how many times 21 can fit into the first part (5). Since 21 does not fit into 5, we move on to the next part.

## Step 4: Division with the second part

Find how many times 21 can fit into the second part (57). Since 21 fits into 57 twice ($$2 \times 21 = 42$$), we write 2 on top of the division bracket above the 7. Then, subtract 42 from 57 and write the difference (15) under the second part of the dividend.

## Step 5: Division with the third part

Now, we combine the difference (15) with the next digit in the dividend(5). Write 155 below the second part of the dividend. Determine how many times 21 can fit into this number (155). Since 21 can fit into 155 seven times ($$7 \times 21 = 147$$), we write 7 on top of the division bracket above the 5. Then, subtract 147 from 155 and write the difference (8) under the combined part of the dividend.

## Step 6: Identify the quotient and remainder

Now that we can't divide the left-over number (8) by 21, we say that our quotient is the number we got above the dividend, which is 27, and remainder is 8. So, upon dividing 575 by 21, we find that the quotient $$q = 27$$ and remainder $$r = 8$$.

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