How Many Factors of 80 are Greater Than\(\sqrt80\)? GMAT Problem Solving

Question: How many factors of 80 are greater than \(\sqrt80\)?

1. Ten
2. Eight
3. Six
4. Five
5. Four

“How many factors of 80 are greater than \(\sqrt80\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Plus 2021”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Approach Solution 1:

The square root condition means we will have to find divisors of (>= 9)

So we will start with 80 and keep dividing till we hit the condition

80 --> can be divided in 2 ways by 2 or by 5 to get (40, 16)

16 --> can not be divided into anything greater than or equal to 9

40 --> can be divided by 2 or by 5 to get 20 and 8. The 8 doesnt count as it is less than 9.

20 --> can be divided by 2 or by 5 to get (10,4). The 4 doesnt count since it is less than 9.

10 --> cant be divided into anything greater than or equal to 9

So we get : 10,20,40,16,80

Hence 5 is the answer 

Correct Answer: D

Approach Solution 2:

We will first see how to find the Number of Factors of an Integer

First make prime factorization of an integer n=\(a ^p*b^q*c^r\), where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1).
NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450
450 = \(2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is
(1+1)(2+1)(2+1) = 2*3*3 = 18 factors.

Now, as per the question:

\(\sqrt80\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.
Now, 80 = 16*5

=>\(2^4\)*5

=>Number of factors of 80 is (4+1)(1+1)
=10
Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.
Correct Answer: D

Approach Solution 3:

80 is greater than 8 and less than 9, hence [square root]80. Therefore, we must determine the number of factors of 80 that are greater than 8.

Now since 80=16+5=24+5, the number of factors for 80 is (4+1)(1+1)=10 (4+1)(1+1)=10 (see below for instructions on how to get an integer's number of factors). Out of these 10, 1, 2, 4, 5, and 8 are the only five variables that are less than or equal to 8. Other 5 components make up more than 8 factors.

Calculating the Amount of an Integer's Factors

Make a prime factorization of the integer n=apbqcr, where the prime factors aa, bb, and cc of nn are and the powers pp, qq, and rr are.

The mathematical expression for the number of components in nn is (p+1)(q+1)(r+1)(p+1)(q+1)(r+1). NOTICE: this will contain both 1 and n.

Example: Finding the number of all factors of 450: 450=\(2^1*3^2*5^2\)

The total number of 450 factors, including 1 and the number 450 itself, is (1+1)(2+1)(2+1)=233=18 factors.

Correct Answer: D

Suggested GMAT Quant Questions

• If 2^98=256L+N, where L and N are integers and 0≤N≤4, what is the value of N? GMAT Problem Solvin
• A draining pipe can empty a pool in 4 hours. GMAT Problem Solving
• If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region? GMAT Problem Solving
• Kate and David each have $10. GMAT Problem Solving
• How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4, and 5 which are divisible by 3, without repeating the digits? GMAT Problem Solving
• Which of the following lines are parallel to line x = 4 – 2y? GMAT Problem Solving
• John has 12 clients and he wants to use color coding to identify each client GMAT Problem Solving
• Which of the following expressions has the greatest values? GMAT Problem Solving
• If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving
• What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6? GMAT Problem Solving
• If 69% of k is 23, approximately how much is 23% of k? GMAT Problem Solving
• Metropolis Corporation has 4 Shareholders GMAT Problem Solving
• If x and y are positive integers and (1/7)^x * (1/8)^12 = (1/8)^1/18y, then what is the value of y-x? GMAT Problem Solving
• At Springfield High, three-fourths of the male students and half of the female students speak a foreign language GMAT Problem Solving
• What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• A conference room is equipped with a total of 45 metal or wooden chairs. GMAT Problem Solving
• A welder received an order to make a 1 million litre cube-shaped tank. GMAT Problem Solving