#### Number properties

**1)**Find the greatest four digit number which is exactly divisible by 393.

**2)** Which of the following numbers is divisible by 22?

**3)** Find the LCM of 368 and 46.

^{4}* 23

Prime factors of 46 = 2 * 23

LCM of 368 and 46 = 2

^{4}* 23 = 368. Hence(d)

**4)** LCM and HCF of two numbers are 504 and 8 respectively. If one of the numbers is 56, find the other number.

504 * 8 = 56 * x. à x= 72. Hence(c)

**5)** One-fifth of two-third of four-seventh of a number is 16. What is 35% of that number?

\({1 \over {5}}({2 \over {3}})\) (\({4x \over {7}}\)) = 16, à x=210\(\)

35% of 210 = 73.5. Hence(b)

**6)** When a number is divided by 43 the remainder is 37. When the same number is divided by 29, what will be the remainder?

R(37/29) = 8. Hence(d)

**7)** When a number is successively divided by 9, 11 and 14, it leaves a remainder 4, 7 and 13 respectively. Find the smallest such number.

_{1}, q

_{2}, q

_{3}are the successive quotients, then x =9q

_{1}+ 4

q

_{1}= 11q

_{2}+ 7, q

_{2}= 14q

_{3}+ 13. The smallest number will be if q

_{3}= 0, N = 1354. Hence(a).

**8)** Find the unit digit of 853^{1327}

Unit digit of 853

^{1327}= 3

^{3}= 27. Hence(c)

**9)** What is the unit digit of 3984^{191} + 4376^{297}

The cyclicity of 6 is 1

Unit digit of 3984

^{191}= 4

Unit digit of 4376

^{297}= 6

Unit digit of 3984

^{191}+ 4376

^{297}= 4 + 6 = 10. Hence(A)

**10)** How many factors are there in 548?

Number of factors = (1+1)*(1+1)*(1+1)*(1+1) = 16 factors. Hence(b).

**11)** Find the product of the factors of 1352.

^{3}*13

^{2}= (3+1) * (2+1) = 12 factors

Product of the factors = N

^{(no of factors /2)}= 1352

^{(12}

^{/2)}à1352

^{6}. Hence (c).

**12)** Find the greatest number of 4 digits which when divided by 7, 9 and 11 leaves 4 as remainder in each case.

Greatest 4 digit number which is divisible by 693 = 9702

Required number = 9702 + 4 = 9706. Hence(d)

**13)** Convert binary to octal (101111011)_{2}

_{2}= 101 | 111 | 011

= (573)

_{8}. Hence(a)

**14)** Find the remainder of 1438^{157} when divided by 5.

^{157}= 8

R(8/5) = 3. Hence (c).

**15)** Find the remainder when 71^{69} divided by 72.

= R(\({72 \over {72}}\)) - R(\({1 \over {72}}\))

= 0 – 1 + 72 = 71. Hence(b).