# How to find HCF / GCD of numbers?

The question is from the topic Number Systems and Number Theory. It is about finding the GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers.

#### Question

Find the G.C.D of 12x

^{2}y

^{3}z

^{2}, 18x

^{3}y

^{2}z

^{4}, and 24xy

^{4}z

^{3}.

- 6xy
^{2}z^{2}
- 6x
^{3}y^{4}z^{3}
- 24xy
^{2}z^{2}
- 24xy
^{3}z^{2}
- 18x
^{2}y^{2}z^{3}

Correct Answer -

**6xy**^{2}z^{2}. Choice (1)

#### Explanatory Answer

G.C.D of 12, 18 and 24 is 6.

Greatest common divisor or highest common factor is found by listing down factors common to all numbers in their respective lowest power and multiplying them.

The factors common to all three numbers are x, y, z and their lowest power amongst all numbers are 1, 2 and 2 respectively.

Therefore, G.C.D = 6xy

^{2}z

^{2}
Correct answer choice (1)

Level of difficulty : Easy to Moderate

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