Find the greatest number which will exactly divide 200 and 320.

• 10

• 20

• 16

• 40

Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.

• 183

• 243

• 483

• 723

H.C.F. of  is

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• 
• 
• 

B.

H.C.F. of 

If the L.C.M. and H.C.F. of two expressions are (x² + 6x + 8) (x + 1) and (x + 1) respectively and one of the expressions is x² + 3x + 2, find the other.

• x² + 5x + 4

• x² - 5x + 4

• x² + 4x + 5

• x² - 4x + 5

A.

x² + 5x + 4

x² + 6x + 8 = x² + 4x + 2x +8 = x(x + 4) + 2(x + 4) = (x + 4) (x + 2)

x² + 3x + 2 = x² + 2x + x +2=  x(x + 2) + 1(x + 2) = (x + 2) (x + 1)
Now, 
First expression x Second expression = LCM X HCF
⟹  (x² + 3x + 2) x Second expression = (x² + 6x + 8) (x + 1) x (x + 1)
⟹ (x + 2) (x + 1) x Second expression = (x + 4) (x + 2) (x + 1) (x + 1)

⟹ (x + 4) (x + 1) = x² + 4x + x + 4 = x² + 5x + 4

 

 

If the students of 9th class are arranged in a row of 6, 8, 12 or 16, no student is left behind. Then the possible number of students in the class is

• 60

• 72

• 80

• 96