Math, asked by surman4762, 9 months ago

What is the greatest number that divide both 55 and 73 leaving remainders of 7 and 9 respectively?

Answers

Answered by pulakmath007
1

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The greatest number that divide both 55 and 73 leaving remainders of 7 and 9 respectively is

= HCF of (55-7) & (73-9)

= HCF of 48 & 64

= 16

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Answered by RvChaudharY50
325

Concept used :-

To find the greatest no. that will divide x, y, z leaving remainders a, b, & c respectively = Required number (greatest divisor) = H.C.F. of (x – a), (y – b) and (z – c).

Solution :-

→ x = 55

→ y = 73

→ a = 7

→ b = 9

So,

Req. Num. = H.C.F. of (x – a) and (y – b)

→ Req. Num. = H.C.F. of (55 - 7) and (73 - 9)

→ Req. Num. = H.C.F. of 48 and 64

Now,

Prime Factors of 48 and 64 :-

48 = 2 * 2 * 2 * 2 * 3

→ 64 = 2 * 2 * 2 * 2 * 2 * 2

HCF = 2 * 2 * 2 * 2 = 16 .

Hence, The Required Number is 16.

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