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Comprehension
Factorization
is the process of breaking down a number or algebraic expression into its
simplest components, called factors. For integers, factorization involves
expressing a number as a product of its prime factors. Two important concepts
related to factorization are the Highest Common Factor (HCF) and the Least
Common Multiple (LCM).
The HCF,
also known as the greatest common divisor, is the largest number that divides
two or more numbers without leaving a remainder. To find the HCF of two
numbers, we factorize each number into its prime factors and multiply the
common factors.
The LCM,
on the other hand, is the smallest number that is a multiple of two or more
numbers. To find the LCM, factorize each number into its prime factors, take
the highest power of each prime that appears in these factorization, and
multiply them together.
Factorization is the process of expressing a number or an algebraic expression as a product of its factors.
Factorize both numbers into their prime factors, identify the common prime factors, and multiply them together.
The product of the HCF and LCM of two numbers equals the product of the numbers themselves.
The HCF of 12 and 18 is 6. (Prime factorization: 12 = 2² × 3, 18 = 2 × 3²; Common factors: 2 × 3 = 6)
The LCM of 4 and 5 is 20. (Prime factorization: 4 = 2², 5 = 5; Highest power of primes: 2² × 5 = 20)
