Question:
What is the least positive integer that is not a factor of \( 25! \) and is not a prime number?
What is the least positive integer that is not a factor of \( 25! \) and is not a prime number?
Show Hint
To find numbers not dividing a factorial, test integers just greater than the factorial’s base number. Factorials cover all smaller integers.
Updated On: Oct 7, 2025
- 26
- 28
- 36
- 56
- 58
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Factors of \( 25! \).
Since \( 25! \) is the product of integers from 1 to 25, every integer up to 25 divides \( 25! \).
Step 2: Numbers greater than 25.
We seek the smallest integer greater than 25 that is not a factor of \( 25! \) and is not prime.
Step 3: Check candidates.
- 26 = \( 2 \times 13 \). Divides \( 25! \). Not correct.
- 27 = \( 3^3 \). Divides \( 25! \). Not correct.
- 28 = \( 2^2 \times 7 \). This does not divide \( 25! \) fully, since 28>25 and is not prime. Hence, 28 is the least.
Step 4: Conclusion.
Thus, the required integer is: \[ \boxed{\text{(B) 28}} \]
Since \( 25! \) is the product of integers from 1 to 25, every integer up to 25 divides \( 25! \).
Step 2: Numbers greater than 25.
We seek the smallest integer greater than 25 that is not a factor of \( 25! \) and is not prime.
Step 3: Check candidates.
- 26 = \( 2 \times 13 \). Divides \( 25! \). Not correct.
- 27 = \( 3^3 \). Divides \( 25! \). Not correct.
- 28 = \( 2^2 \times 7 \). This does not divide \( 25! \) fully, since 28>25 and is not prime. Hence, 28 is the least.
Step 4: Conclusion.
Thus, the required integer is: \[ \boxed{\text{(B) 28}} \]
Was this answer helpful?
0
0
Top GRE Quantitative Aptitude Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions
Top GRE Number System Questions
- How many integers from 3 to 30, inclusive, are odd?
- The greatest prime factor of 144 is \( x \)
The greatest prime factor of 96 is \( y \) - Dharik lives in a house on a straight street. For years, there have been 16 houses on his street to the right of his house and 17 houses on his street to the left of his house. Last year, 5 new houses were built on the same street even further to the left of those houses to the left of Dharik’s house. If these are the only houses on this street, how many houses are on this street?
- Let \( p = 4 \times 6 \times 11 \times n \), where \( n \) is a positive integer. Compare the following:
Quantity A: Remainder when \( p \) is divided by 5
Quantity B: Remainder when \( p \) is divided by 33 - How many five-digit numbers can be formed using the digits 0, 2, 3, 4 and 5, when repetition is allowed, such that the number formed is divisible by 2 or 5 or both?
View More Questions
Top GRE Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions