Question

find hcf of 5^13 and 2 ^26​

Answer 1

Given:

number 1:$2^{56}$

number 2: $2^{56}$

To find:

HCF of the two numbers

Solution:

To find the Highest Common Factor of two numbers, we first break the numbers into their respective prime factors in the multiplied form and then multiply the common prime factors.

If the numbers have no common factor, then the HCF of such numbers is 1.

So,

$2^{56}$ can be broken into the multiplication of 2 with 2, 56 times.

And, $5^{13}$ can be broken into the multiplication of 5 with 5, 13 times.

Now 2 and 5 being prime numbers themselves, any power of 2 and 5 will only produce a series of 2's and 5's respectively. Now, 2 and 5 have no common factor and cannot be broken down further.

So, their HCF is 1, and so HCF of $5^{13}$ and $2^{56}$ will also be 1.

Hence, HCF of $2^{56}$ and $2^{56}$ is 1.