If two positive integers a and b are written as $a = x^{3} y^{2}$ and $b = x y^{3}; x, y$ are prime numbers, then HCF (a, b) is

x y

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x y^{2}

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x^{3} y^{3}

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x^{2} y^{2}

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Solution

The correct option is A $x y^{2}$
$H C F (H i g h e s t c o m m o n f a c t o r) : - (A l s o c a l l e d a s G C D) H C F o f t w o n u m b e r s i s t h e n u m b e r w h i c h c o m l e t e l y d i v i d e s (w i t h 0 r e m a i n d e r) b o t h t h e n u m b e r s . F o r e x a m p l e, H C F o f 14 a n d 21 i s 7, H C F (54, 27) i s 27. G i v e n a = x^{3} y^{2}, b = x y^{3} I t c a n b e o b s e r v e d t h a t x y^{2} i s a c o m m o n f a c t o r o f b o t h a a n d b . H e n c e H C F (a, b) = x y^{2} .$

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If two positive integers a and b are written as $a = x^{3} y^{2} a n d b = x y^{2}$ where x, y are prime numbers, then HCF (a, b) is

A) $x y$
B) $x y^{2}$
C) $x^{3} y^{3}$
D) $x^{2} y^{2}$

Q. If two positive integers a and b are written as

a = x^{3} y^{2}

and

b = x y^{3}; x, y

are prime numbers , then HCF(a,b) is

(a) xy (b) xy² (c) x³y³ (d) x²y²

Q. Two positive integers a and b can be written as a = x³y² and b = xy³, where x, y are prime numbers. Find LCM (a, b).

Q. Two positive integers a and b can be written as a = x³y² and b = xy³, where x and y are prime numbers. Find HCF(a, b) and LCM(a, b).

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If two positive integers a and b are written as a=x3y2 and b=xy3;x,y are prime numbers, then HCF (a, b) is

The correct option is A xy2HCF(Highestcommonfactor):−(AlsocalledasGCD)HCFoftwonumbersisthenumberwhichcomletelydivides(with0remainder)boththenumbers.Forexample,HCFof14and21is7,HCF(54,27)is27.Givena=x3y2,b=xy3Itcanbeobservedthatxy2isacommonfactorofbothaandb.HenceHCF(a,b)=xy2.

If two positive integers a and b are written as $a = x^{3} y^{2}$ and $b = x y^{3}; x, y$ are prime numbers, then HCF (a, b) is