To find the remainder when 32 32 32 is divided by 7, we first need to clarify what we mean by 32 32 32. In this case, it is interpreted as the number formed by placing 32 three times next to each other, which can be expressed as 323232.
The next step is to find the remainder of 323232 when divided by 7. We can do this by simplifying the number under modulo 7. However, a more efficient way is to break down the number:
323232 = 320000 + 3200 + 32
Now we calculate each part modulo 7:
– For 320000: We first find 320000 ÷ 7. The integer part of that division is approximately 45714, which gives us a remainder of 320000 – (45714 * 7) = 320000 – 319998 = 2.
– For 3200: Similarly, we perform 3200 ÷ 7. The integer part is approximately 457, and the remainder is 3200 – (457 * 7) = 3200 – 3199 = 1.
– For 32: Finally, 32 ÷ 7 gives an integer part of 4, and the remainder is 32 – (4 * 7) = 32 – 28 = 4.
Now, we can combine these remainders:
Remainder = 2 + 1 + 4 = 7
Since we are asked for the remainder when divided by 7, we take the result modulo 7.
Thus, the final remainder when 323232 is divided by 7 is 0.