Question

find HCF and LCM of following pair of integer by applying the fundamentals theorem of arithmetic. 225, 867​

Answer 1

$\underline { \pink { Fundamental \: Theorem \: of \: Arithmetic }}$

Every composite number can be expressed (factorised) as a product of primes , and this Factorisation is unique , apart from the order in which the prime factors occur.

$We \:have$

$225 = 3 \times 3 \times 5 \times 5 = 3^{2}\times 5^{2}$

$867 = 3 \times 17\times 17 = 3^{1}\times 17^{2}$

$HCF (225,867) = 3^{1} = 3$

/* Product of the smallest power of each common prime factors of the numbers */

$LCM ( 225, 867 ) = 3^{2} \times 5^{2} \times 17^{2} \\= 65025$

/* product of the greatest power of each prime factors of the numbers */

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