The sum of the first two digits of a three digit number is 4. The sum of the numbers
that is formed by using each digit of the number once is 1998. If the number has 8
factors, then what is the number?
Answers
The sum of the first two digits of a three digit number is 4.
The sum of the numbers that is formed by using each digit of the number once is 1998.
The number has 8 factors.
The number.
Let the three digit number be abc.
A/q,
a + b = 4 . . .(i)
Again, the sum of the numbers which are by using each digit of the number once is 1998.
According to the above given statement, we get :-
Putting the places' value and adding further :-
→ 100a + 10b + c + 100a + 10c + b + 100b + 10a + c + 100b + 10c + a + 100c + 10a + b + 100c + 10b + a = 1998
→ 200a + 200b + 200c + a + 10a + a + b + 10b + b + c + 10c + c = 1998
→ 200a + 22a + 200b + 22b + 200c + 22c = 1998
→ 222a + 222b + 222c = 1998
→ a + b + c = 9
Putting the value of a + b from equation (i) :-
4 + c = 9
→ c = 5
Possible values for a and b (c = 5):
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
The required number could be :-
135, 225 or 315
A/q, the required number must have 8 factors.
◘ 135 is the only number which has 8 factors.
So, a = 1 and b = 3.
Again, putting the places' value and adding in abc :-
abc = 100a + 10b + c
→ abc = 100(1) + 10(3) + 5
→ abc = 100 + 30 + 5
→ abc = 135
Hence, the answer is 135.
GIVEN:−
The sum of the first two digits of a three digit number is 4.
The sum of the numbers that is formed by using each digit of the number once is 1998.
The number has 8 factors.
TO FIND:−
The number.
SOLUTION:−
Let the three digit number be abc.
A/q,
a + b = 4 . . .(i)
Again, the sum of the numbers which are by using each digit of the number once is 1998.
According to the above given statement, we get :-
abc+acb+bac+bca+cab+cba=1998
Putting the places' value and adding further :-
→ 100a + 10b + c + 100a + 10c + b + 100b + 10a + c + 100b + 10c + a + 100c + 10a + b + 100c + 10b + a = 1998
→ 200a + 200b + 200c + a + 10a + a + b + 10b + b + c + 10c + c = 1998
→ 200a + 22a + 200b + 22b + 200c + 22c = 1998
→ 222a + 222b + 222c = 1998
→ a + b + c = 9
Putting the value of a + b from equation (i) :-
4 + c = 9
→ c = 5
Possible values for a and b (c = 5):
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
The required number could be :-
135, 225 or 315
A/q, the required number must have 8 factors.
◘ 135 is the only number which has 8 factors.
So, a = 1 and b = 3.
Again, putting the places' value and adding in abc :-
abc = 100a + 10b + c
→ abc = 100(1) + 10(3) + 5
→ abc = 100 + 30 + 5
→ abc = 135
Hence, the answer is 135.
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