Question

the G.C.D of 2*4 × 3*2,2*3×5*2 and 3*3×5*4 is
a.1
b.2
c.3
d.4

Answer 1

Answer:

GCD = Greatest Common Divisor.

x

3

−1=(x−1)(x

2

+xy+y2) {identity a

3

−b

3

and a

2

−b

2

}

x

4

−1=(x

2

−1)(x

2

+1)

=(x−1)(x+1)(x

2

+1)

GCD=(x−1)

Step-by-step explanation:

I hope it's help you dear please make me brainliests

Answer 2

Concept

The greatest common divisor (gcd) of two or more numbers is the greatest common divisor that divides them exactly. This is also known as the highest common factor (HCF). For example, the greatest common divisor of 15 and 10 is 5. Both numbers are divisible by 5.

Given

We have been given the prime factorization of three numbers    

 $2^4\times3^2\ , 2^3\times5^2 \ , 3^3\times5^4$

Find

We are asked to determine the GCD of given numbers.

Solution

The prime factorization method writes any number  as a product of prime numbers and finds the product of the least powers of each common prime factor.

The given prime factorization is $2^4\times3^2\ , 2^3\times5^2 \ , 3^3\times5^4$ .

From the factorization, we can see, that there is no common prime factor so ,only 1 will be the common prime factors.

This method is only applicable to positive numbers, i.e. natural numbers.

Therefore ,  the GCD of given numbers is 1 which is option (a) .

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