7 Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
8. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.
Answers
Step-by-step explanation:
445−4=441
572−5=567
699−6=693
The greatest common factors of 441, 567 and 693 is,
441=3×3×7×7
567=3×3×3×3×7
693=3×3×7×11
The common factors are 3×3×7=63.
63
445
=7 with remainder as 4.
63
572
=9 with remainder as 5.
63
699
=11 with remainder as 6.
Therefore, 63 is the greatest number.
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Answer:
7) answer 63
8) answer 17
Step-by-step explanation:
7)
Answer
445−4=441
572−5=567
699−6=693
The greatest common factors of 441, 567 and 693 is,
441=3×3×7×7
567=3×3×3×3×7
693=3×3×7×11
The common factors are 3×3×7=63.
63
445
=7 with remainder as 4.
63
572
=9 with remainder as 5.
63
699
=11 with remainder as 6.
Therefore, 63 is the greatest number.
8)Deducting the remainders from numbers we get,
398−7=391
436−11=425
542−15=527
H.C.F of these new numbers is the largest possible number that divides 398,436,542 leaving respective remainders
391=17×23
425=17×5
2
527=17×31
∴ Answer = H.C.F(391,425,527)=17