Question

If hcf of 144 and 180 are expressed in the form 13m -3,find the value of m.

Answer 1

Answer:

Step-by-step explanation:

144 = 2 ^ 4 * 3 ^ 2

180= 2 ^ 2 * 5 * 3 ^ 2

∴H.C.F ( 180,144) = 2 ^ 2 * 3 ^ 2 = 4 * 9 = 36

∴13m - 3 = 36

⇒13m = 39

⇒m = 3

∴m = 3

Answer 2

The value of ‘m’ is 3.

To find:

Value of m

Solution:

Given: H.C.F. of 144 and 180 is expressed in form of 13m–3.

H.C.F. of 144 and 180 is as under:

$144=12 \times 12=2 \times 2 \times 2 \times 2 \times 3 \times 3$

$180=10 \times 18=2 \times 2 \times 5 \times 3 \times 3$

Hence, H.C.F. of $144 \text { and } 180=2 \times 2 \times 3 \times 3=36$

H.C.F. of 144 and 180 is mentioned as 13m–3 in the question. So,

$13 m-3=36$

$13 \mathrm{m}=36+3$

$13 \mathrm{m}=39$

$m=\frac{39}{13}$

$\mathrm{m}=3$