What is the greatest number that divide both 55 and 73 leaving remainders of 7 and 9 respectively?
Answers
Answered by
1
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
Answered by
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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