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If the numbers 296, 436 and 542 divided by a positive number 'p' leaving the remainder 7, 11 and 15 respectively, then find the largest value of p.

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If the numbers 296, 436 and 542 divided by a positive number 'p' leaving the remainder 7, 11 and 15 respectively, then find the largest value of p.

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1 Answer

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k1 p + 7 = 296 

k2 p + 11 = 436 

k3 p + 15 = 542 

k1 p = 289 = (17) (17) 

k2 p = 425 = (17) (25)

k3 p = 527 = (17) (31)

Hence p is 17

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