# HCF Important Formulas, Definitions, & Examples:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Number System Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

#### What is HCF?

HCF stands for Highest Common Factor. The HCF of two or more numbers is the highest positive integer that can divide each of the two or more numbers. The HCF is also known as the Greatest Common Divisor (GCD). The value HCF is always positive.

#### What is HCF of 10 and 15?

Answer: 5 is the highest common factor of 10 and 15. Here, 5 is the highest positive integer that can divide 10 and 15.

#### What is HCF of 2 and 3?

Answer: The HCF of 2 and 3 is 1. Here 1 is the highest positive integer that can divide 2 and 3 exactly.

#### What is GCF of 32 and 2?

Answer: The GCF of 32 and 2 is 2. Here 2 is the highest positive integer that can divide 32 and 2 exactly.

#### What is HCF of 6, 9, and 12?

Answer: 3 is the highest common factor of 6, 9, and 12. Here, 3 is the highest positive integer that can divide 6, 9, and 12 exactly.

#### How to find HCF?

The HCF of smaller numbers can be found easily but, what if we need to find the HCF of bigger numbers. We can follow the given process to find the HCF of bigger numbers.

Step (1): Factorize the numbers into their prime factors.

Step (2): Collect all the common factors with their minimum available power.

Step (3): Multiply the collected factors to get the HCF.

#### What is the HCF of 10, 25, and 50?

Solution: Step(1): Factorize the numbers into their prime factors.$$10 = 2 \times 5 = 2^{1} \times 5^{1}$$ $$25 = 5 \times 5 = 5^{2}$$ $$50 = 2 \times 5 \times 5 = 2^{1} \times 5^{2}$$ Step(2): Collect all the common factors with their minimum available power.$$= 5^{1}$$ Step(3): Multiply the collected factors.$$= 5$$ Here, 5 is the highest positive number that can divide 10, 25, and 50 exactly.

#### How to find the HCF of fractions?

We know that fractions always have two parts, Numerator and Denominator. The fraction is written in the form of $$\frac{Numerator}{Denominator}$$. Here the denominator should not be zero. The HCF of fractions can be found by using the below formula.

$$HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}$$

$$HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}$$

#### What is the HCF of $$\frac{6}{7}$$ and $$\frac{8}{9}$$?

Solution:

$$HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}$$

$$HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}$$

$$HCF = \frac{HCF \ of \ (6,8)}{LCM \ of \ (7,9)}$$ $$= \frac{2}{63}$$

#### What is the HCF of $$\frac{4}{5}$$ and $$\frac{7}{8}$$?

Solution:

$$HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}$$

$$HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}$$

$$HCF = \frac{HCF \ of \ (4,7)}{LCM \ of \ (5,8)}$$ $$= \frac{1}{40}$$

#### Practice Unsolved Questions

What is the HCF of 24 and 36?

What is the HCF of 2 and 4?

What is the HCF of 3 and 5?

What is the HCF of 3 and 9?

What is the HCF of 15 and 20?

What is the HCF of 18 and 24?

What is the GCF of 30 and 2?

What is the GCF of 35 and 2?

What is the GCF of 36 and 2?

What is the GCF of 38 and 2?

What is the HCF of 2, 3, and 1?

What is the HCF of 2, 3, and 5?

What is the HCF of 15, 25, and 30?