Find the largest number which divides …
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Sia ? 6 years, 5 months ago
The given numbers are 320 and 457
Now as 5 and 7 are remainders on division of 320 and 457 by said number
On subtracting the reminders 5 and 7 from 320 and 457 respectively we get:
320 - 5 = 315,
457 - 7 = 450
The prime factorization:of 315 and 405 are
{tex}315 = 3 \times 3 \times 5 \times 7{/tex}
{tex}= 3 ^ { 2 } \times 5 \times 7{/tex}
{tex}450 = 2 \times 3 \times 3 \times 5 \times 5{/tex}
{tex}= 2 \times 3 ^ { 2 } \times 5 ^ { 2 }{/tex}
{tex}\therefore{/tex} H.C.F. of 315 and 450 = {tex}3 ^ { 2 } \times 5 = 9 \times 5 = 45{/tex}
Hence the said number =45
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