How many 3 digit numbers are there whose sum of digits is equal to product of digits? 2022-11-29 16:15:14
How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?
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- How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?Answer (Detailed Solution Below) 21How many 3 digit numbers are there for which the product of their digits?What 3 numbers is the sum and product equal?How many threeHow many 3 digit numbers can you find such that product of their digits is a natural number less than 5?
Answer (Detailed Solution Below) 21
Free
Reading Comprehension Vol 1
12
Questions 36 Marks 20 Mins
Calculation:
Let the 3-digit number be abc,
⇒ a × b × c = 3 or 4 or 5 or 6
a × b × c =
3
4
5
6
Possibilities
(113, 131, 311)
(122, 212, 221)
(115, 151, 511)
(123, 132, 231)
(114, 141, 411)
(116, 161, 611)
(213, 321, 312)
⇒ Total numbers = 3 + 6 + 3 + 9 = 21
∴ There are 21 digits whose products of their digits is more than 2 but less than 7.
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2-digit numbers:
Solutions: a = 0, b = 0 & a = 2, b = 2
22 |—–> 2 + 2 = 4 = 2 * 2
3-digit numbers:
123 |—–> 1 + 2 + 3 = 6 = 1 * 2 * 3
Also true for 132, 213, 231, 312, 321
4-digit numbers:
1124 |—–> 1 + 1 + 2 + 4
= 8 = 1 * 1 * 2 * 4
1142 |—–> 1 + 1 + 4 + 2 = 8 = 1 * 1 * 4 * 2
And other combinations of 1, 1, 2 and 4
5-digit numbers:
11125 |—–> 1 * 1 * 1 * 2 * 5 = 10 = 1 + 1 + 1 + 2 + 5
11152 |—–> 1 * 1 * 1 * 5 * 2 = 10 = 1 + 1 + 1 + 5
+ 2
And other combinations of 1, 1, 1, 2 and 5
11133 |—–> 1 * 1 * 1 * 3 * 3 = 9 = 1 + 1 + 1 + 3 + 3
And other combinations of 1, 1, 1, 3 and 3
11222 |—–> 1 * 1 * 2 * 2 * 2 = 8 = 1 + 1 + 2 + 2 + 2
And other combinations of 1, 1, 2, 2 and 2
6-digit numbers:
111126
|—–> 1 * 1 * 1 * 1 * 2 * 6 = 12 = 1 + 1 + 1 + 1 + 2 + 6
111162 |—–> 1 * 1 * 1 * 1 * 6 * 2 = 12 = 1 + 1 + 1 + 1 + 6 + 2
And other combinations of 1, 1, 1, 1, 6 and 2
112411 |—–> 1 * 1 * 2 * 4 * 1 * 1 = 8 = 1 + 1 + 2 + 2 + 1 + 1
And other combinations of 1, 1, 2, 4, 1 and
1
7-digit numbers:
1111127 |—–> 1 * 1 * 1 * 1 * 1 * 2 * 7 = 14 = 1 + 1 + 1 + 1 + 1 + 2 + 7
1111172 |—–> 1 * 1 * 1 * 1 * 1 * 7 * 2 = 14 = 1 + 1 + 1 + 1 + 1 + 7 + 2
And other combinations of 1, 1, 1, 1, 1, 2 and 7
1111134 |—–> 1 * 1 * 1 * 1 * 1 * 3 * 4 = 12 = 1 + 1 + 1 + 1
+ 1 + 3 + 4
1111143 |—–> 1 * 1 * 1 * 1 * 1 * 4 * 3 = 12 = 1 + 1 + 1 + 1 + 1 + 4 + 3
And other combinations of 1, 1, 1, 1, 1, 3 and 4
8-digit numbers:
11111128 |—–> 1 * 1 * 1 * 1 * 1 * 1 * 2 * 8 = 16 = 1 + 1 + 1 + 1 + 1 + 1 + 2 + 8
11111182 |—–> 1 * 1 * 1 * 1 * 1 * 1 * 2 * 8 = 16 = 1 + 1 + 1 + 1 +
1 + 1 + 2 + 8
And other combinations of 1, 1, 1, 1, 1, 1, 2 and 8
9-digit numbers:
111111129 |—–> 1 * 1 * 1 * 1 * 1 * 1 * 1 * 2 * 9 = 18 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 9
111111192 |—–> 1 * 1 * 1 * 1 * 1 * 1 * 1 * 9 * 2 = 18 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 9 + 2
And other combinations of 1, 1, 1, 1, 1, 1, 1, 2 and 9
111111135
|—–> 1 * 1 * 1 * 1 * 1 * 1 * 1 * 3 * 5 = 15 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 3 + 5
111111153 |—–> 1 * 1 * 1 * 1 * 1 * 1 * 1 * 5 * 3 = 15 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 5 + 3
And other combinations of 1, 1, 1, 1, 1, 1, 1, 3 and 5
10-digit numbers:
1*1*1*1*1*1*1*1*x*y = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + x + y
x * y = 8 + x + y, with 0 ≤ x, y ≤ 9
so I get x = y = 4
1111111144
|—–> 1*1*1*1*1*1*1*1*4*4 = 16 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 4 + 4
And other combinations of 1, 1, 1, 1, 1, 1, 1, 1, 4 and 4
Question: Generalize this.
How many 3 digit numbers are there for which the product of their digits?
Solution: The product of the digits of the three-digit numbers should be more than 2 and less than 7 . Hence the possible numbers are as follows. Hence there are a total of 21 possibilities.
What 3 numbers is the sum and product equal?
1, 2 and 3 are the requires whole numbers whose sum and product is same. Q..
How many three
Answer. Explanation: Answer: 25 three-digit multiples of 18 have the sum of the digits also equal 18.
How many 3 digit numbers can you find such that product of their digits is a natural number less than 5?
The possibilities are (114), (122), (141), (212), (221) and (411) i.e. no. of ways equal to 6. ∴ total number of ways for product to be less than 5 = 1 + 3 + 3 + 6 ⇒ 13 ways.
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