Published: 21 Jun 2019

**1. Factor and Multiples :**

Factoring is like taking a number apart. It means to express a number as the product of its factors. Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite). The number 12 is a multiple of 3, because it can be divided evenly by 3. 3 x 4 = 12.

**2. Highest common factor (H.C.F) or Greatest Common Measure (G. C. M) or Greatest Common Divisor (G. C. D) :**

The least number which is exactly divisible by each of the given numbers is called the least common multiple of those numbers. The H.C.F of two or more then two numbers is the greatest number that divides each of them exactly.

There are two methods of finding the H.C.F of a given set of numbers :

* 1. Factorization Method :* Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

* Steps 1:* Find all the factors of each given number.

Finding the H.C.F of more than two numbers : Suppose we have to find the H.C.F. of three numbers. Then, H.C.F. of three given numbers.

Similarly, the H.C.F. of more than given numbers may be obtained.

**3. Last Common Multiple (L.C.M) :**

The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

* 1. Factorization Method of Finding L.C.M :* Resolve each of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.

**4. Product of two numbers = Product of their H.C.F and L.C.M.**

**5. C-primes : Two numbers are said to be co-primes if their H.C.M is 1.**

**6. H.C.F and L.C.M. of Fraction :**

* 1. H.C.F.* = H.C.F.of Numerators / L.C.M.of Denominators

*7. H.C.F. and L.C.M of Decimal Fractions :*

In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers without decimal point, find H.C.F or L.C.M as the case may be. Now. In the result, mark off as many decimal places as are there in each of the given numbers.

Steps to solve H.C.F. and L.C.M. of decimals:

* Step 1:* Convert each of the decimals to like decimals.

**8. Comparison of Fractions :**

Find the L.C.M of the denominators of the given fractions, Convert each of the fractions into an equivalent fraction with L.C.M as the denominator, by multiplying both the numerator and denominator by the same number. The resultant fraction with the greatest numerator is the greatest.

There are two main ways to compare fractions:

1. Using * decimals*,

2. Using the

Quantitative Aptitude Arithmetical Ability - H.C.F & L.C.M of Numbers (1)