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The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)
Correct answer is '180'. Can you explain this answer?
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The number of 5-digit natural numbers, such that the product of their ...
Factors of 36 = 22⋅ 32⋅ 1
Five-digit combinations can be
(1, 2, 2, 3, 3) (1, 4, 3, 3, 1), (1, 9, 2, 2, 1)
(1, 4, 9, 1, 1) (1, 2, 3, 6, 1) (1, 6, 6, 1, 1)
i.e., total numbers
Five-digit combinations can be
(1, 2, 2, 3, 3) (1, 4, 3, 3, 1), (1, 9, 2, 2, 1)
(1, 4, 9, 1, 1) (1, 2, 3, 6, 1) (1, 6, 6, 1, 1)
i.e., total numbers
= (30 × 3) + 20 + 60 + 10 = 180
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The number of 5-digit natural numbers, such that the product of their ...
Approach:
To find the number of 5-digit natural numbers whose product of digits is 36, we need to consider all the possible combinations of digits that multiply to 36.
Prime Factorization of 36:
36 = 2^2 * 3^2
So, the possible combinations of digits are {1, 1, 2, 2, 3, 3, 6}.
Counting the Combinations:
Now, we need to consider the placement of these digits in a 5-digit number.
Since the number is 5-digit, we need to have exactly 5 digits.
- If we use one 6, then we have 5 positions to place the remaining 4 digits. So, the number of ways = 5! / 2! = 60 ways.
- If we don't use 6, then we have 4 positions to place the remaining 4 digits. So, the number of ways = 4! = 24 ways.
Total Number of 5-digit Numbers:
Total number of 5-digit numbers = Number of ways with 6 + Number of ways without 6
= 60 + 24
= 84
However, since we are asked for the total number of 5-digit natural numbers, the answer should also consider the fact that the 5-digit number cannot start with 0.
Therefore, the first digit has 9 choices (1-9).
So, the total number of 5-digit natural numbers = 9 * 84 = 756
Thus, the number of 5-digit natural numbers, such that the product of their digits is 36, is 756.
To find the number of 5-digit natural numbers whose product of digits is 36, we need to consider all the possible combinations of digits that multiply to 36.
Prime Factorization of 36:
36 = 2^2 * 3^2
So, the possible combinations of digits are {1, 1, 2, 2, 3, 3, 6}.
Counting the Combinations:
Now, we need to consider the placement of these digits in a 5-digit number.
Since the number is 5-digit, we need to have exactly 5 digits.
- If we use one 6, then we have 5 positions to place the remaining 4 digits. So, the number of ways = 5! / 2! = 60 ways.
- If we don't use 6, then we have 4 positions to place the remaining 4 digits. So, the number of ways = 4! = 24 ways.
Total Number of 5-digit Numbers:
Total number of 5-digit numbers = Number of ways with 6 + Number of ways without 6
= 60 + 24
= 84
However, since we are asked for the total number of 5-digit natural numbers, the answer should also consider the fact that the 5-digit number cannot start with 0.
Therefore, the first digit has 9 choices (1-9).
So, the total number of 5-digit natural numbers = 9 * 84 = 756
Thus, the number of 5-digit natural numbers, such that the product of their digits is 36, is 756.
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The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer?
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The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer?.
The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)Correct answer is '180'. Can you explain this answer?.
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