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CBSE - X
Fundamental Theorem of Arithmetic
Fundamental Theorem of Arithmetic states that:
Every composite number can be expressed or factorised as a product
of prime numbers and this factorisation is unique except in the
order of the prime factors.
We can write the prime factorisation of a number in the form of powers of its prime factors.
By expressing any two numbers as their prime factors, their highest common factor (HCF) and lowest common multiple (LCM) can be easily calculated.
The HCF of two numbers is equal to the product of the
terms containing the least powers of common prime factors of
the two numbers.
The LCM of two numbers is equal to the product of the terms
containing the greatest powers of all prime factors of the two
numbers.
Note that the product of the given numbers is equal to the product of
their HCF and LCM. This result is true for all positive
integers and is often used to find the HCF of two given numbers
if their LCM is given and vice versa.
