Question

The HCF of 2²×3³×5²,2³×3²×5²×7 and 2⁴×3⁴×5×7²×11 is:​

Answer 1

Step-by-step explanation:

answer mate hope it helps you

Answer 2

HCF is 180.

Given:

• Prime factors of three numbers.
• ${2}^{2} \times {3}^{3} \times {5}^{2}$
• ${2}^{3} \times {3}^{2} \times {5}^{2} \times 7$
• ${2}^{4} \times {3}^{4} \times {5} \times {7}^{2} \times 11$

To find:

• Find the HCF of numbers.

Solution:

Concept/formula to be used:

HCF: Choose the highest common factor,i.e. the prime numbers which are present in all numbers having the same exponent.

Step 1:

Analyze the prime factors of given numbers.

In all three numbers, It is clear that prime numbers 2,3 and 5 are present in each number.

We have to take the powers of 2,3 and 5 which is common in all.

We cannot take 7 and 11 because these are not present in all numbers.

Step 2:

Find HCF of numbers.

$HCF({2}^{2} \times {3}^{3} \times {5}^{2}, \: {2}^{3} \times {3}^{2} \times {5}^{2} \times 7, \: {2}^{4} \times {3}^{4} \times {5} \times {7}^{2} \times 11) = {2}^{2} \times {3}^{2} \times 5$

$HCF({2}^{2} \times {3}^{3} \times {5}^{2}, \: {2}^{3} \times {3}^{2} \times {5}^{2} \times 7, \: {2}^{4} \times {3}^{4} \times {5} \times {7}^{2} \times 11) = 4 \times 9 \times 5$

$\bf HCF({2}^{2} \times {3}^{3} \times {5}^{2}, \: {2}^{3} \times {3}^{2} \times {5}^{2} \times 7, \: {2}^{4} \times {3}^{4} \times {5} \times {7}^{2} \times 11) = 180$

Thus,

The HCF of numbers is 180.

Learn more:

1) FIND THE H.C.F. OF 26 AND 91 BY PRIME FACTORISATION METHOD...

https://brainly.in/question/19449495

2) Hcf of 32 and 144 by prime factorization

https://brainly.in/question/12188837

#SPJ2