6. Find the Prime Factorization of 4641
7. Three bells toll at intervals of 9, 12, 15 minutes. If they start tolling together, after what time will they next toll together?
8. The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.
9. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, find the other number.
10. Find the greatest number which divides 134 and 167 leaving 2 as remainder in each case.
Answers
Answer:
Step-by-step explanation:
Q6 factorize(4641) = 3 x 7 x 13 x 17
Q7 LCM (9, 12,15) = 3×3×2×2×5 = 180 So, the LCM of 9, 12 and 15 is 180. The bells will toll together after 180 minutes or 3 hours. Answer) Bells will toll together after 180 minutes or 3 hours.
Q8 To find the length of the longest tape which can measure the three dimensions of the room, we need to find the H.C.F of length, breadth and height of the room respectively.
Length of the room = 825 cm
Breadth of the room = 675 cm
Height of the room = 450 cm
Let us factorize all three given dimensions.
825 = 3 × 5 × 5 × 11
675 = 3 × 3 × 3 × 5 × 5
450 = 2 × 3 × 3 × 5 × 5
Hence, 3, 5 and 5 are the common prime factors here.
So, H.C.F =3 × 5 × 5
H.C.F = 75 cm
Therefore, we need 75 cm the longest tape to measure the three dimensions of the room.