Question

divide:
overline{549enclose{longdiv}{903,690}} r square

Explanation:

Step1: Perform long division

We divide 903690 by 549. First, we see how many times 549 goes into 903 (the first three digits of the dividend). 549 1 = 549, 549 2 = 1098 which is too big. So we start with 1. But actually, we can use the division algorithm: \( 903690 \div 549 \). Let's do the division step by step.

First, calculate \( 903690 \div 549 \). Let's simplify the division. We can divide numerator and denominator by 3: \( 903690 \div 3 = 301230 \), \( 549 \div 3 = 183 \). Now divide 301230 by 183. Again, divide by 3: \( 301230 \div 3 = 100410 \), \( 183 \div 3 = 61 \). Now we have \( 100410 \div 61 \).

Calculate \( 61 \times 1646 = 61\times(1600 + 46)=61\times1600 + 61\times46 = 97600 + 2806 = 100406 \). Then \( 100410 - 100406 = 4 \). Wait, maybe better to do the original division.

Alternatively, use a calculator approach: \( 549 \times 1646 = 549\times(1600 + 40 + 6)=549\times1600 + 549\times40 + 549\times6 = 878400 + 21960 + 3294 = 878400+21960=900360+3294=903654 \). Then the remainder is \( 903690 - 903654 = 36 \). Wait, no, let's check again.

Wait, the dividend is 903690. Let's do 549 1646: 5491600=878400, 54940=21960, 5496=3294. Sum: 878400+21960=900360+3294=903654. Then 903690 - 903654 = 36. Wait, but maybe my initial simplification was wrong. Let's do the division properly.

Long division steps:

1. 549 into 903 (first three digits of 903690). 549*1=549, subtract from 903: 903 - 549=354. Bring down 6 (next digit) to make 3546.

1. 549 into 3546: 549*6=3294. Subtract: 3546 - 3294=252. Bring down 9 to make 2529.

1. 549 into 2529: 549*4=2196. Subtract: 2529 - 2196=333. Bring down 0 to make 3330.

1. 549 into 3330: 549*6=3294. Subtract: 3330 - 3294=36.

So the quotient is 1 (from first step) followed by 6 (second), 4 (third), 6 (fourth)? Wait, no, the number of digits: the dividend is 6 digits (903690), divisor is 3 digits. So 903690 ÷ 549. Let's count the digits: 5491000=549000, 5492000=1098000 which is too big. So quotient is a 4-digit number? Wait, 5491600=878400, 5491646=903654 as above. So quotient is 1646, remainder 36. Wait, but let's check 549*1646 + 36 = 903654 + 36 = 903690. Yes. So the quotient is 1646 and remainder 36. Wait, but in the problem, the dividend is 903,690 (maybe a typo, 903690). So the division is 903690 ÷ 549.

Step2: Verify the division

We can check by multiplying the quotient and divisor and adding the remainder: \( 549 \times 1646 + 36 \). As calculated before, \( 549 \times 1646 = 903654 \), and \( 903654 + 36 = 903690 \), which matches the dividend. So the quotient is 1646 and the remainder is 36.

Answer:

Quotient: 1646, Remainder: 36