Question

using fundamental theorem of arithmetic find the HCF and LCM of 306 and 657 also verify that HCF multiply LCM equal to product of numbers

Answer 1

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Answer 2

Answer:

The HCF and LCM are  9 and 22338

Step-by-step explanation:

Given two numbers 306 and 657

we have to find the HCF and LCM using Fundamental Theorem of Arithmetic method

The fundamental theorem of arithmetic, also called the unique factorization theorem

The prime factorization of above three numbers are

$306=2\times 3\times 3\times 17$

$657=3\times 3\times 73$

$LCM(306 and 657 )=2\times 3 \times 3 \times 17 \times 73= 22338$

$HCF=3\times 3=9$

The HCF and LCM are 9 and 22338

Verification:

$LCM\times HCF=\text{Product of numbers}$

$9\times 22338=306\times 657$

$201042=201042$

Verified