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Test the divisibility of the following numbers by 8
(i) 9364
(ii) 2138
(iii) 36792
(iv) 901674
(v) 136976
(vi) 1580184
Test the divisibility of the following numbers by 11
(i) 3443
(ii) 13728
(iii) 11366
(iv) 137269
(v) 153109
(vi) 8790322
Find the greatest number which divides 134 and the 167 leaving 2 as remainder
The product of two number is 2160 and their HCF is 12. The LCM of these numbers is
Three bells toll together at intervals 9, 12, 15 minutes. They start tolling together. At what interval of time will they toll together again
Three bells toll at intervals  9min , 12 min and 15min.
So, if they start tolling together, they will ring together at LCM ( 9,12,15)
So, We have to find LCM of 9 , 12 and 15.
9 = 3×3
12 = 2×2×3
15 = 3×5
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.
Bells will toll together after 180 minutes or 3 hours.
Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are
Let the required numbers be x, 2x, 3x.
Then, their H.C.F =x. so, x= 12
Therefore, The numbers are 12, 24, 36
The sum of two numbers is 528 and their HCF is 33. The number of pairs of numbers satisfying the above condition is
Let the required numbers be 33a and 33b.
Then 33a +33b= 528 ⇒ a+b = 16.
Now, coprimes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
Therefore, Required numbers are (33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4
The product of two numbers is 4107. If the HCF of these numbers is 37 then the greatest number is
Three numbers which are coprime to each other are such that the product of first two is 551 and that of the last two is 1073. The sum of the three numbers is
Three numbers are in the ratio of 3 : 4 : 5 and their LCM is 2400. Their HCF is
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
The HCF and LCM of two numbers are 21 and 84 respectively. If the ratio of the two numbers be 1 : 4, the larger of the two numbers is
If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case, then sum of the digits in N is
N = H.C.F. of (4665  1305), (6905  4665) and (6905  1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54. Is
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes how many times do they toll together
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