Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 14949 by Tinkutara last updated on 05/Jun/17

Find the largest prime factor of 203203. Anyone please suggest the method without calculators or log tables.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{prime}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{203203}. \\ $$$$\mathrm{Anyone}\:\mathrm{please}\:\mathrm{suggest}\:\mathrm{the}\:\mathrm{method} \\ $$$$\mathrm{without}\:\mathrm{calculators}\:\mathrm{or}\:\mathrm{log}\:\mathrm{tables}. \\ $$

Commented by RasheedSoomro last updated on 05/Jun/17

203203=203000+203=203(1000+1) =203×1001. Only factorizing, not the largest prime. But now 203 and 1001 can be more easily factorized with normal trial method.And after that selecting the lorgest is easy one. 203=29×7 1001=13×11×7 The largest is 29

$$\mathrm{203203}=\mathrm{203000}+\mathrm{203}=\mathrm{203}\left(\mathrm{1000}+\mathrm{1}\right) \\ $$$$=\mathrm{203}×\mathrm{1001}.\:\mathrm{Only}\:\mathrm{factorizing},\:\mathrm{not} \\ $$$$\mathrm{the}\:\mathrm{largest}\:\mathrm{prime}.\:\mathrm{But}\:\mathrm{now}\:\mathrm{203}\:\mathrm{and} \\ $$$$\mathrm{1001}\:\mathrm{can}\:\mathrm{be}\:\mathrm{more}\:\mathrm{easily}\:\mathrm{factorized} \\ $$$$\mathrm{with}\:\mathrm{normal}\:\mathrm{trial}\:\mathrm{method}.\mathrm{And}\:\mathrm{after}\: \\ $$$$\mathrm{that}\:\mathrm{selecting}\:\mathrm{the}\:\mathrm{lorgest}\:\mathrm{is}\:\mathrm{easy}\:\mathrm{one}. \\ $$$$\mathrm{203}=\mathrm{29}×\mathrm{7} \\ $$$$\mathrm{1001}=\mathrm{13}×\mathrm{11}×\mathrm{7} \\ $$$$\mathrm{The}\:\mathrm{largest}\:\mathrm{is}\:\mathrm{29} \\ $$

Commented by Tinkutara last updated on 06/Jun/17

Thanks Sir!

$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com