HCF & LCM - Practice Set 2

 Q1. 468 can be expressed as a product of prime as a) 2×2×13×7×2×3 b) 2×2×13×7 c) 2×2×13×3×3 d) 2×2×3×3 ×7 e) None of these

Q2. A number n is said to be perfect if the sum of all its divisor (excluding n itself ) is equal to n. An example of a perfect number is:

a) 27 b) 35 c) 21 d) 6 e) None of these

Q3. ⁷⁰¹⁰⁵/₂₁₀₃₅ when expressed in simplest form is
a) ²⁰³/601 b) ²⁰⁰³/603 c) ²⁰⁰³/601 d) ²⁰⁰¹/603 e) None of these

Q4. H.C.F. of 2²×3³×5⁵, 2³×3²×5²×7 and 2⁴×3⁴×7²×5×11 is :
a)22×32×5
b)22×32×5×7×11
c)24×34×55
d)24×34×55×7×11
e) None of these

Q5. 5²×3×2⁴×2²×3²×7 Find the L.C.M.
a) 12300 b) 12600 c) 24600 d) 25200

Q6. H.C.F. of 4×27×3125, 8×9×25×27 & 16×81×5×11×49 is:
a) 180 b) 360 c) 540 d) 1260 e) None of these

Q7. The greatest 5-digit number that is exactly divisible by 100 is:
a) 99899 b) 99800 c) 99900 d) 99889 e) None of these

Q8. What will be the remainder when (29)³⁶ is divided by 28 ?
a) 0 b) 1 c) 29 d) 5 e) Cannot be determined

Q9. A number when divided by 627 leaves a remainder 43. By dividing the same number by 19, the remainder will be
a)19 b) 24 c) 43 d) 5 e) 13

Q10. The numbers 1, 3, 5 ... 25 are multiplied together. The number of zeroes at the right end of the product is :
a) 22 b) 8 c) 13 d) 6 e) 0

Q11. When a certain number is multiplied by 21, the product consist oof only fours. The smallest such number is:
a) 21164 b) 4444 c) 444444 d) 444 e) None of these

Q12. In a question, divisor is 2/3 of the dividend and twice the remainder. If the remainder is 5, then the dividend is
a) 85 b) 145 c) 225 d) 65 e) None of these

Solution

(1)
Sol : Option (c)

2✘2✘13✘3✘3 = 468

(2)
Sol : Option (d)

n	Divisors excluding n	Sum of divisor
27	3✘9✘1	13
35	5✘7✘1	13
21	3✘7✘1	11
6	3✘2✘1	6

(3)
Sol : Option (c)

(4)

Sol: Option (a)

(5)

Sol:Option (d)

50+75+150+250+350

=875

(6)

Sol: Option (a)

4✘27✘3125=2³✘3³✘5⁵

8✘9✘25✘7=2³✘3²✘5^2✘7 

16✘81✘5✘11*49=2⁴✘3⁴✘7²✘5✘11

 H.C.F. = 2²✘3²✘7 = 180

(7)

Sol: Option (c)

(8)

Sol: Option (b)

(9)

Sol: Option (d)

(10)

Sol: Option (e)

(11)

Sol: Option (a)

(12)

Sol: Option (e)