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. |

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.

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

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

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

**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.

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.

**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.

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.

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

\(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

**Solution:**

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

\(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

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

**Solution:**

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

\(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

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

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?

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
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Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
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