an integer is divided by 8 giving a remainder of 3 the resulting quotient when divided by 7 gives a remainder of 2. the resulting quantity is then divided by 7 giving a quotient of 1 and remainder of 6. what will the finale remainder be if the order of the divisors is reversed?
Answers
Answer:
Final remainder=7
Step-by-step explanation:
Given below
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The final remainder is 7.
Given:
An integer is divided by 8 giving a remainder of 3 the resulting quotient when divided by 7 gives a remainder of 2.
The resulting quantity is then divided by 7 giving a quotient of 1 and remainder of 6.
To find:
Final Remainder
Solution:
Let the first integer be x and quotient be y.
For first equation:
Integer = x
Quotient = y
Remainder = 3
Divisor = 8
For second equation:
Integer = y
Quotient = z
Remainder = 2
Divisor = 7
For third equation:
Integer = z
Quotient = 1
Remainder = 6
Divisor = 7
According to division algorithm
z = 7(1) + 6
z = 13
Putting z into second equation,
13(7) + 2 = y
y = 93.
Putting y into first equation
93(8) + 3 = x
x = 747
Now, dividing 747 by 7 and then repeating the process 3 times.
When 747 is divided by 7
Divisor = 7
Quotient = 106
Remainder = 5
When 106 is divided by 7
Divisor = 7
Quotient = 15
Remainder = 1
When 15 is divided by 8
Quotient = 1
Remainder = 7
So, the final remainder is 7.
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