Final answer:
To find the respective remainders when the order of divisors is reversed, we can use the Chinese Remainder Theorem. By solving the congruences, we find that the respective remainders are 89 modulo 8, 89 modulo 5, and 89 modulo 3.
Step-by-step explanation:
To find the remainders when the order of divisors is reversed, we can use the Chinese Remainder Theorem. We know that the number gives a remainder of 1 when divided by 3, a remainder of 4 when divided by 5, and a remainder of 7 when divided by 8. With this information, we can find the respective remainders when the order of divisors is reversed.
To solve this problem, we can start by finding the number that satisfies the given remainders. The Chinese Remainder Theorem tells us that such a number exists and is unique modulo the product of the three divisors.
In this case, the product of the three divisors is 3 * 5 * 8 = 120. So, we need to find the number x that is congruent to 1 modulo 3, congruent to 4 modulo 5, and congruent to 7 modulo 8.
By solving these congruences, we can find that x ≡ 89 (mod 120). So, the respective remainders when the order of divisors is reversed are 89 modulo 8, 89 modulo 5, and 89 modulo 3.