Find the largest number which exactly divides 280 and 1245 and leaves remainders of 4 and 3

Asked by Priyaanshu Roy | 22nd May, 2014, 10:27: AM

Expert Answer:

I t space i s space g i v e n space t h a t space o n space d i v i d i n g space 1245 space b y space t h e space r e q u i r e d space n u m b e r space t h e r e space i s space a space r e m a i n d e r space o f space 4. T h a t space i s space 1245 minus 5 equals 1241 space i s space e x a c t l y space d i v i s i b l e space b y space t h e space r e q u i r r e d space n u m b e r. S i m i l a r l y comma space 280 minus 3 equals 277 space i s space a l s o space e x a c t l y space d i v i s i b l e space b y space t h e space r e q u i r e d space n u m b e r. T h u s comma space t h e space r e q u i r e d space n u m b e r space i s space t h e space H C F space o f space 1241 space a n d space 277. L e t space u s space n o w space f i n d space t h e space H C F space o f space 1241 space a n d space 277 space b y space e u c l i d apostrophe s space a l g o r i t h m. 1241 equals 4 cross times 277 plus 133 277 equals 2 cross times 133 plus 11 133 equals 12 cross times 11 plus 1 11 equals 11 cross times 1 plus 0 T h u s space 1 space i s space H C F space o f space 1241 space a n d space 133 space a n d space h e n c e space 1 space i s space t h e space r e q u i r e d space n u m b e r.

Answered by Vimala Ramamurthy | 22nd May, 2014, 11:20: AM

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