Question

find out the hcf of 3^5,3^9 and 3^14​

Answer 1

highest common factor is 3^5 only.

because it's only the least power of 3

Answer 2

$3^5$ is the highest common factor

Solution:

Given that,

We have to find highest common factor of $3^5\:,\:3^9\:,\:3^{14}$

Step 1:

Break down every term into factors

$3^5 = 3^5\\\\3^9 = 3^2 \times 3^2 \times 3^5\\\\3^{14} =3^3 \times 3^3 \times 3^3 \times 3^5$

Step 2:

Look for factors that appear in every single term to determine the highest common factor

Here,

$3^5$ is the highest common factor

Learn more:

Find the common factors of the terms (i) 12x, 36 (ii) 2y, 22xy (iii) 14pq, 28p^2q^2 (iv) 2x, 3x^2, 4 (v) 6abc, 24ab^2, 12a^2b (vi) 16x^3, −4x^2, 32x (vii) 10pq, 20qr, 30rp (viii) 3x^2y^3, 10x3y^2, 6x^2y^2z

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