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If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?
- a)121
- b)3267
- c)363
- d)33
- e)None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If both 112and 33are factors of the number a * 43* 62* 1311, then what...
Step 1: Prime factorize the given expression
a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311
Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33
112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'
33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.
The question is "what is the smallest possible value of 'a'?"
The smallest value that 'a' can take is 363
The smallest value that 'a' can take is 363
Choice C is the correct answer.
Most Upvoted Answer
If both 112and 33are factors of the number a * 43* 62* 1311, then what...
Factors of the given number
- The number in question is a * 43 * 62 * 1311.
- We are given that both 112 and 33 are factors of this number.
Finding the smallest possible value of a
- To find the smallest possible value of a, we need to find the common factors of the given number with 112 and 33.
- Factors of 112 are 1, 2, 4, 8, 14, 16, 28, 56, 112.
- Factors of 33 are 1, 3, 11, 33.
- We need to find the common factors of 112, 33, and the given number.
Common factors of 112, 33, and the given number
- The common factors of 112, 33, and the given number are 1 and 33.
- Since we are looking for the smallest possible value of a, a must be the smallest common factor, which is 33.
Smallest possible value of a
- Therefore, the smallest possible value of a is 33.
- Hence, the correct answer is option 'C' - 363.
- The number in question is a * 43 * 62 * 1311.
- We are given that both 112 and 33 are factors of this number.
Finding the smallest possible value of a
- To find the smallest possible value of a, we need to find the common factors of the given number with 112 and 33.
- Factors of 112 are 1, 2, 4, 8, 14, 16, 28, 56, 112.
- Factors of 33 are 1, 3, 11, 33.
- We need to find the common factors of 112, 33, and the given number.
Common factors of 112, 33, and the given number
- The common factors of 112, 33, and the given number are 1 and 33.
- Since we are looking for the smallest possible value of a, a must be the smallest common factor, which is 33.
Smallest possible value of a
- Therefore, the smallest possible value of a is 33.
- Hence, the correct answer is option 'C' - 363.
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