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### Course Content

##### HCF and LCM

The smallest four digit number is divisible by 6,8 and 16 is

1000

1002

1004

1008

Find the greatest number which will divide 223 and 1083 leaving remainder of 8 in both case

25

40

43

47

Find the greatest number which will divide 201 adn 671 leaving remainder 6 and 8 respectively

15

51

39

65

### Other questions

What is the greatest number which will divide 33 and 168 leaving the remainder 3 in both cases?

15

13

17

14

Solutions

33–3 = 30
168–3 = 165
here hcf 30 and 165 is 15

What is the greatest number that divides 926 and 2,313, leaving 2 and 3 as remainders, respectively?

213

462

426

345

Solutions

926 - 2 = 924
2313-3 = 2310.
HCF of 924 and 2310 is 231

What is the largest number that can divide 410,751,1030 leaving 7 as a remainder in each case?

31

21

47

34

Solutions

410 – 7 = 403 , 751–7=744 , 1030 – 7 = 1023
Required number=HCF of 403 ,744 and 1023.
HCF=31

What is the largest number which divides 62, 132, 237 to leave same remainder in each case?

31

42

35

54

Solutions

Let us say that the number 'd' divides 62, 132, and 237 to leave the remainder 'r'
62 - r, 132 - r, and 237 - r are divisible by 'd'
(132 - r) - (62 - r) and (237 - r) - (132 - r) are divisible by 'd'
70 and 105 are divisible by 'd'
HCF of 70 and 105 = d = 35

What is the greatest number which will divide 33 and 168 leaving the remainder 3 in both cases?

14

15

16

17

Solutions

168–3 = 165
33–3 = 30
HCF of 30 and 165 is 15

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