# GRE® Math Practice Q3

#### Number Theory | Select One or More Answers | Common Factors and HCF

The GRE maths select one or more answers question given below is from the topic number properties. It tests the concept of finding the Common Factors of a set of numbers by finding out the factors of the HCF of those numbers.

Question 3: Which of the following numbers are factors common to 108, 288, and 396?
Indicate all such numbers

1. 72
2. 24
3. 36
4. 8
5. 12
6. 9

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### Explanatory Answer | GRE Quant Question 3

#### Step 1: Compute the HCF of the three numbers

Prime factorize 108, 288, and 396
108 = 22 × 33
288 = 25 × 32
396 = 22 × 32 × 11

HCF is the product of the lowest power of common prime factors of the numbers.
HCF(108, 288, 396) = 22 × 32 = 36

#### Step 2: List down all the factors of the HCF(108, 288, 396)

HCF(108, 288, 396) = 36
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
From the given options, 9, 12, and 36 are factors common to all the three numbers.
Choices C, E, and F are the factors common to all the three numbers.

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