Question

HCF of 2 cube into 3 square into 5, 2 square into 3 cube into 5 square and 2^4 into 3 into 5 cube into 7 is

Answer 1

Answer:

HCF=product of common terms with lowest power

Step-by-step explanation:

=(2'2*3*5)=(4*3*5)=60

Answer 2

HCF of the numbers = 60

Correct question : HCF of 2³ × 3² × 5 , 2² × 3³ × 5² , 2⁴ × 3 × 5³ × 7 is

Given :

2³ × 3² × 5 , 2² × 3³ × 5² , 2⁴ × 3 × 5³ × 7

To find :

The HCF of the numbers

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

Solution :

Step 1 of 3 :

Write down the given numbers

Here the given numbers are 2³ × 3² × 5 , 2² × 3³ × 5² , 2⁴ × 3 × 5³ × 7

Step 2 of 3 :

Find each common prime factor in the numbers

First number = 2³ × 3² × 5

Second number = 2² × 3³ × 5²

Third number = 2⁴ × 3 × 5³ × 7

2 , 3 , 5 are the prime numbers present in the prime factorisation of first number

2 , 3 , 5 are the prime numbers present in the prime factorisation of second number

2 , 3 , 5 , 7 are the prime numbers present in the prime factorisation of third number

So common prime factors in the given numbers are 2 , 3 , 5

Step 3 of 3 :

Calculate HCF of the numbers

Smallest power of 2 = 2

Smallest power of 3 = 1

Smallest power of 5 = 1

Hence the required HCF of the numbers

= Product of smallest power of each common prime factor in the given numbers

= 2² × 3¹ × 5¹

= 60

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