H.C.F (Highest Common Factor) = H.C.F of two or more than two numbers is the product of highest number of common factors
L.C.M(Lowest Common multiple)= The L.C.M of two or mire than two numbers id the product of the highest powers of all the prime factors
Results
#1. Which of the following has most number of divisors?
Which of the following has most number of divisors?
99=1*3*3*11
101=1*101
176=1*2*2*2*2*11
182=1*2*7*13
divisors of 99 are 1,3,9,11,33,99
divisors of 101 are 1 and 100
divisors of 176 are 1,2,4,8,16,22,44,88 and 176
divisors of 182 are 1,2,7,13,14,26,91 and 182
176 has most number of divisors.
#2. 1095/1168 when expressed in simplest form is :
H.C.F of 1095 and 1168=73
1095/1168=1095÷73/1168÷73=15/16
#3. H.C.F of 4*27 *3125,8*9*25*7&16*81*5*11*49 is
H.C.F of 4*27 *3125,8*9*25*7&16*81*5*11*49 is
4*27 *3125=2²*3³*5⁵;8*9*25*7=2³*3²*5²*7
16*81*5*11*49=2⁴*3⁴*5*7²*11
H.C.F=2²*3²*5=180
#4. Find the highest common factor of 36 and 84.
Find the highest common factor of 36 and 84.
36=2*3
84=2²*3²*7
H.C.F =2²*3=12
#5. which of the following is a pair of co- primes?
which of the following is a pair of co- primes?
H.C.F of 18 and 25 is 1
so they are co- primes
#6. Find the lowest common multiple of 24,36 and 40.
Find the lowest common multiple of 24,36 and 40.
L.C.M =2*2*2*3*3*5=360
#7. The H.C.F of 1.75,5.6 and 7 is
The H.C.F of 1.75,5.6 and 7 is
175/100, 56/10, 7
7/4, 28/5,7
35
0.35
#8. The L.C.M of 3,2.7 and 0.09 is
The L.C.M of 3,2.7 and 0.09 is
L.C.M of 300,270,9 is 2700
27.00=27
#9. Three number are in the ratio of 3:4:5 and their L.C.M is 2400. Their H.C.F is :
Three number are in the ratio of 3:4:5 and their L.C.M is 2400. Their H.C.F is :
Let the number is 3x , 4x , 5x
L.C.M = 60x= 2400
x=40
the number are (3*40 ) ,(4*40) &(5*40)
#10. The L.C.M of two numbers is 495 and their H.C.F is 5 . If the sum of the numbers is 10 then their difference is
The L.C.M of two numbers is 495 and their H.C.F is 5 . If the sum of the numbers is 10 then their difference is
Let the numbers be x and (100- x )
x(100-x)=5*495
x^2-100x 2475=0
(x-55)(x-45)=0
x=55 or x=45
required number =55-45=10
#11. Product of two co- prime numbers is 117. Their L.C.M should be :
Product of two co- prime numbers is 117. Their L.C.M should be :
H.C.F of Co- prime numbers is 1
so L.C.M =117/1
=117
#12. The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M.?
The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M.?
H.C.F of two numbers divides their L.C.M
8 is not factor of 60
#13. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case
requied number = H.C.F of (91-43), (183-91), and (183-43)
= H.C.F of 48,92 and 140
= 4
#14. Which is the following fractions is the largest?
L.C.M of 8,16,40 and 80 =80
7/8=70/80
113/16=65/80
31/40=62/80
70/80>63/80>65/80>62/80
7/8 is largest
#15. The least multiple of 7 , which leaves a remainder of 4 when divided by 6,9,15 and 18 is
LCM= 6,9,15 and 18= 90
number 90k 4 which is multiple of 7
least value of of k for which (90K 4) is divisible by 7 is k =4
required number is =90*4 4=364
#16. The greatest number of four digits which is divisible by 15,25,40 and 75 is
The greatest number of four digits which is divisible by 15,25,40 and 75 is
greatest number of 4 digits is 9999.LCM of 15,25,40 and 75 is 600
9999/600=remainder =399
9999-399=9600
required number 9600
#17. The H.C.F of two numbers is 11 and their L.C.M is 693. If one of the numbers is 77 find the other
The HCF of two numbers is 11 and their LCM is 693. If one of the numbers is 77 find the other
other number =(118693/77)=99
#18. Two number are in the ratio of 15:11. If their H.C.F is 13 find the numbers
let 15x and 11x
hCF=13
(15*13) and (11*13)
195 and 143
#19. The L.C.M of 2/3, 3/5, 4/7, 9/13 is :
The L.C.M of 2/3, 3/5, 4/7, 9/13 is :
L.C.M= L.C.M of 2,3,4,9/H.C.F of 3,5,7,13
36
#20. 252 can be expressed as a product of prime as :
252 can be expressed as a product of prime as :
Answer = 2*2*3*3*7