Question
The number is successively divided by 5, 7, 11 give remainder as 3, 1, 10.
If last quotient is 114.
Find the numbers.
If last quotient is 114.
Find the numbers.
Answers
mathhelper
I will attempt the simplest approach:
numbers which when divided by 5 leave a remainder of 3 :
8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, ...
numbers which when divided by 7 leave a remainder of 1
8, 15, 22, 29, 36, 43, 50, 57, 64, ....
numbers which when divided by 11 leave a remainder of 10
10, 21, 32, 43, 54 ...
ahhh, notice 43 satisfies all 3 conditions.
This was lucky, if the number had been larger, this method would become
impractical. In that case I had hinted in another reply that I would use
"The Chinese Remainder Theorem"
btw, if we multiply the divisors, and then add or subtract multiples of
that product we get another number that satisfies.
so 5*7*11 = 385
which means 43+385 or 428 would also work , you can check it !
so possible answers are 43 + k(385) , where k is a whole number.
numbers which when divided by 5 leave a remainder of 3 :
8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, ...
numbers which when divided by 7 leave a remainder of 1
8, 15, 22, 29, 36, 43, 50, 57, 64, ....
numbers which when divided by 11 leave a remainder of 10
10, 21, 32, 43, 54 ...
ahhh, notice 43 satisfies all 3 conditions.
This was lucky, if the number had been larger, this method would become
impractical. In that case I had hinted in another reply that I would use
"The Chinese Remainder Theorem"
btw, if we multiply the divisors, and then add or subtract multiples of
that product we get another number that satisfies.
so 5*7*11 = 385
which means 43+385 or 428 would also work , you can check it !
so possible answers are 43 + k(385) , where k is a whole number.
Kaur
Sorry dear
Didn't understand
Kindly explain in another way
Please
Didn't understand
Kindly explain in another way
Please
mathhelper
I don't understand that you "don't understand"
I gave you the simplest and most direct way of doing this.
I repeat my simple way:
I will attempt the simplest approach:
numbers which when divided by 5 leave a remainder of 3 :
8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, ...
numbers which when divided by 7 leave a remainder of 1
8, 15, 22, 29, 36, 43, 50, 57, 64, ....
numbers which when divided by 11 leave a remainder of 10
10, 21, 32, 43, 54 ...
ahhh, notice 43 satisfies all 3 conditions.
It said find the numbers, I assumed you wanted more than just the 43.
That's where the last part comes in.
I gave you the simplest and most direct way of doing this.
I repeat my simple way:
I will attempt the simplest approach:
numbers which when divided by 5 leave a remainder of 3 :
8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, ...
numbers which when divided by 7 leave a remainder of 1
8, 15, 22, 29, 36, 43, 50, 57, 64, ....
numbers which when divided by 11 leave a remainder of 10
10, 21, 32, 43, 54 ...
ahhh, notice 43 satisfies all 3 conditions.
It said find the numbers, I assumed you wanted more than just the 43.
That's where the last part comes in.