What is the smallest number which when divided by 35, 105 and 175 gives a remainder of 5 each time
Answers
Step-by-step explanation:
The smallest number which, when divided by 35, 56 and 105, leaves a remainder of 5.
Let the number be N. The number N can be written in the following ways.
N = 35x + 5 —(1)
N = 56y + 5 —(2)
N = 105z + 5 —(3)
where x,y and z are whole numbers.
Substracting eqn(1) from eqn(2) we get,
0 = 56y-35x,
i.e 56y = 35x,
i.e 8y = 5x —(4)
Similarly subtracting eqn(1) from eqn(3), we get,
0 = 105z - 35x,
i.e 35x = 105z
x = 3z —(5)
The minimum values of x, y and z satisfying eqn (4) and (5) by trial and error method is x=24, y=15 and z=8.
Substituting z in eqn(3), we get,
N = 105*8 + 5
N = 845
Answer:
Correct answer is 845
Step-by-step explanation:
The factors are
35 = 5x7
56 = 2x2x2x7
105 = 3x5x7
LCM = 2x2x2x3x5x7x= 840
Next add 5 to 840 to 845 as the answer you desire.
Check: 845/35 = 24 as quotient and 5 as remainder. Correct.
845/56 = 15 as quotient and 5 as remainder. Correct.
845/105 = 8 as quotient and 5 as remainder. Correct.
Answer is 845.