LCM and HCF
 The greatest number by which 2300 and 3500 are divided leaving the remainders of 32 and 56 respectively, is

View Hint View Answer Discuss in Forum
As we know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 2300 – 32 = 2268 and 3500 – 56 = 3444Correct Option: D
As we know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 2300 – 32 = 2268 and 3500 – 56 = 3444
∴ HCF = 84
Hence , Required number = 84
 There are 24 peaches, 36 apricots and 60 bananas and they have to be arranged in several rows in such a way that every row contains the same number of fruits of only one type. What is the minimum number of rows required for this to happen ?

View Hint View Answer Discuss in Forum
Minimum number of rows = Maximum number of fruits in each row
∴ HCF of 24, 36 and 60 = 12∴ Minimum number of rows = 24 + 36 + 60 12 12 12
Correct Option: C
Minimum number of rows = Maximum number of fruits in each row
∴ HCF of 24, 36 and 60 = 12∴ Minimum number of rows = 24 + 36 + 60 12 12 12
Hence , Minimum number of rows = 2 + 3 + 5 = 10
 Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers exact number of times is

View Hint View Answer Discuss in Forum
Greatest capacity of measuring vessel
= HCF of 403 litres, 434 litres and 465 litres
First of all we find HCF of 403 and 434
Again , HCF of 31 and 465Correct Option: A
Greatest capacity of measuring vessel
= HCF of 403 litres, 434 litres and 465 litres
First of all we find HCF of 403 and 434
Again , HCF of 31 and 465
∴ Greatest capacity of measuring vessel = 31 litres
 The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively, is

View Hint View Answer Discuss in Forum
We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896
H.C.F = 16Correct Option: B
We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896
H.C.F = 16
Hence , required answer = 16.
 84 Maths books, 90 Physics books and 120 Chemistry books have to be stacked topic wise. How many books will be there in each stack so that each stack will have the same height too ?

View Hint View Answer Discuss in Forum
As the height of each stack is same,
The required number of books in each stack = HCF of 84, 90 and 120
84 = 2 × 2 × 3 × 7
90 = 2 × 3 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5
∴ HCF = 2 × 3 = 6Correct Option: C
As the height of each stack is same, the required number of books in each stack
= HCF of 84, 90 and 120
84 = 2 × 2 × 3 × 7
90 = 2 × 3 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5
∴ HCF = 2 × 3 = 6
Hence , The required number of books in each stack is 6 .