By Team Aakash Byju's

Tips and Tricks to Understand Real Numbers | CBSE Maths Class 10

Euclid’s Division Lemma states that for any two integers a and b, there exists a unique pair of integers q and r such that

Simply the lemma stated as:

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Euclid’s Division Lemma method is significant to find the HCF of 2 numbers, consider 2 integers a and b where a > b.

We use Euclid’s Division Lemma to determine two integers q and r such that

If the remainder is equal to zero, the H.C.F is b, if not, we can use Euclid’s Division Lemma to b (divisor) and r (remainder) to obtain different pairs of quotient and remainder.

The divisor for this step is the H.C.F of the provided set of integers and the process is continued until the remainder of zero is attained.

If the order of the prime factors is neglected, the prime factorisation of any integer is always unique.

Example:

Relation between LCM and HCF is for two positive integers a and b.

Example:

HCF of two numbers is 4, LCM of two numbers is 36 and one of the numbers is 3, find the other number.

Here are some interesting results of Number theory:

The sum or difference of the rational number and an irrational number results in an irrational number.

The product and quotient of the non-zero rational number and irrational number are irrational numbers.