Question: How many positive factors do 180 and 96 have in common?

1. 6
2. 12
3. 16
4. 18
5. 24

Solution and Explanation:

Approach Solution (1):

The question talks about finding the common positive factors of two numbers. The common factors should have its prime numbers in the power which is present in both the original numbers. Hence our first step would be to prime factorize the original numbers
Once we prime factorize the number we can look at the common prime factors of the number along with their powers to find out the common factors
Prime factorizing 180 and 96 would give us 180 = \(2^2*3^2*5\) and \(96=2^5*3\)

From the above prime factorization of 180 and 96, we can analyze that the common factors of 180 and 96 would come from a combination of \(2^1 and 3^1\).
Thus there are 3 * 2 = 6 possible combinations i.e. 6 common factors of 180 and 96
The common factors would be 1, 2, 3, 4, 6 and 12 which are the factors of HCF (180, 96) = 12

Correct Option: A

Approach Solution (2):

The number of common factors will be same as the number of factors of the Highest Common Factor (HCF)
HCF of 180 and 96 = 12
Number of factors of 12 = 6

Correct Option: A

Approach Solution (3):

To find the number of common factors of two integers:

(1) Find the greatest common divisor (GCD) of the two integers;
(2) Find the number of factors of that GCD.

GCD of 180 and 96 is 12 = \(2^2*3\)

The number of factors of 12 is (2 + 1) (1 + 1) = 6

Correct Option: A

“How many positive factors do 180 and 96 have in common?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. 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.

Suggested GMAT Problem Solving Samples

• A Merchant has 1000 kg of Sugar Part of Which He Sells at 8% Profit 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
• \((\frac{1}{7})^x*(\frac{1}{8})^{12}=(\frac{1}{8})^{18y}\) , 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
• Simplify:\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75} GMAT Problem Solving
• There are 6 points on xy-plane GMAT Problem Solving
• Mike, Tom, and Walt are working as sales agents for an insurance company GMAT Problem Solving
• A Commonwealth condominium complex has k apartments, n of which are rented at s dollars a month, providing total monthly revenue of p dollars GMAT Problem Solving
• The Figure Below Shows a Square Inscribed in a Circle with the Radius of√6. What is the Area of the Shaded Region? GMAT Problem Solving
• What is the value of k if the sum of consecutive odd integers from 1 to k equals 441? GMAT Problem Solving
• A circle with a radius R is inscribed into a square with a side K GMAT Problem Solving
• Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts GMAT Problem Solving
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), For Every n≥1, Then a11 Equals GMAT Problem Solving
• The Hexagon ABCDEF is Regular GMAT Problem Solving
• If x is not equal to zero, and x + 1/x = 3, then what is the value of x^4 + 1/x_4? GMAT Problem Solving
• If mn ≠ 0 and 25 Percent of n Equals 37 1/2 Percent of m, What is the Value of 12n/m? GMAT Problem Solving
• How many multiples of 7 are there between 21 and 343, exclusive? GMAT Problem Solving
• How many odd factors does 210 have? GMAT Problem Solving
• How many three-digit integers are not divisible by 3? GMAT Problem Solving
• How many three-digit numbers are there such that all three digits are different and the first digit is not zero? GMAT Problem Solving
• After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible? GMAT Problem Solving
• \(\frac{15^{11}-15^{10}}{14}=?\) GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
• GMAT Problem Solving - Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards
• A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving
• What Is The Circumference Of The Semicircle In The Figure Shown? GMAT Problem Solving
• How Many Odd Factors does 210 have?
• If 80 Lamps Can Be Lighted, 5 Hours Per Day For 10 Days For $21.25
• A Circle with a Radius R is Inscribed into a Square with a Side K.
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year?
• After 6 games, Team B had an average of 61.5 points per game GMAT Problem Solving 
• Simplify:\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75} GMAT Problem Solving 
• There are 6 points on xy-plane GMAT Problem Solving 
• Mike, Tom, and Walt are working as sales agents for an insurance company GMAT Problem Solving 
• What is the value of k if the sum of consecutive odd integers from 1 to k equals 441? GMAT Problem Solving 
• A circle with a radius R is inscribed into a square with a side K GMAT Problem Solving 
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving 
• A farm has chickens, cows and sheep GMAT Problem Solving 
• If g is an integer what is the value of (-1)^g^4-1? GMAT Problem Solving 
• If the equation |x|+|y|= 5 encloses a certain region on the graph GMAT Problem Solving
• If x = ¾ and y = ⅖ , what is the value of (x^2+ 6x+ 9) - (y^2-2y+ 1)? GMAT Problem Solving
• If a Carton Containing a Dozen Mirrors is Dropped GMAT Problem Solving
• The Sun is Approximately 1,400 Million Kilometers from the Planet GMAT Problem Solving
• In a Market, the Price of Medium Quality Mangoes is Half that of Good Mangoes GMAT Problem Solving