Question

find the gcd of 16x³y² , 24 xy³z step by step explanation is needed​

Answer 1

Answer:

Given:-

• 16x³y²
• 24 xy³z

Solution:-

Prime factorising 16x³y² and 24 xy³z.

16x³y²=2×2×2×2×x×x×x×y×y

24 xy³z=2×2×2×3×x×y×y×y×z

We get 8,x and y² as common .

Hence,

GCD= 8xy².

Answer 2

Answer:

Required GCD is 8xy².

Step-by-step explanation:

Here given numbers are 16x³y² , 24 xy³z

We want to find GCD of these numbers.

HCF means Highest Common Factor.

By one examples we can understand this concept more easily.

We are taking four numbers 20,50,70,100.

By prime factorisation,

$20 = 2 \times 2 \times 5 \\ 50 = 2 \times 5 \times 5 \\ 70 = 2 \times 5 \times 7 \\ 100 = 2 \times 2 \times 5 \times 5$

Here highest common factor of 20,50,70 and 100 is

$(2 \times 5) = 10$

So, GCD of 20,50,70 and 100 is 10.

Here numbers are 16x³y² , 24 xy³z

By prime factorisation,

$16 {x}^{3} {y}^{2} = 2 \times 2 \times 2 \times 2 \times x \times x \times x \times y \times y$

and

$24x {y}^{3} z = 2 \times 2 \times 2 \times 3 \times \: x \times y \times y \times y \times z$

So, GCD of 16x³y² , 24 xy³z is

$2 \times 2 \times 2 \times x \times y \times y \\ = 8x {y}^{2}$

Know more about HCF,

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