Question

if the HCF of 1440 & 180 is expressed in the form of 13 m-3, find the value of n. plzzz help ​

Answer 1

Step-by-step explanation:

Given -

• Numbers 1440 and 180

To Find -

• HCF of 1440 and 180 which is expressed in the form of 13m - 3.

Now,

1440 = 2 × 2 × 3 × 2 × 2 × 3 × 2 × 5

180 = 2 × 2 × 3 × 3 × 5

HCF = 12 × 5 × 3 = 180

LCM = 180 × 8 = 1440

Now, Expressing 180 in the form of 13m - 3

→ 13m - 3 = 180

→ 13m = 183

→ m = 183/13

Hence,

The value of m is 183/13

Verification :-

• LCM × HCF = product of two numbers

→ 180 × 1440 = 180 × 1440

→ 259200 = 259200

LHS = RHS

Hence,

Verified..

It shows that our answer is absolutely correct

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ m = 183/13

$\large\underline\mathrm{Given:-}$

• Numbers 1440 and 180

$\large\underline\mathrm{To \: find}$

• HCF of 1440 and 180 which is expressed in the form of 13m - 3.

$\large\underline\mathrm{Solution}$

$\large\underline\mathrm{HCF \: => \: 2 \: × \: 2 \: × \: 3 \: × \: 2 \: × \: 2 \: × \: 3 \: × \: 2 \: × \: 5}$

$\large\underline\mathrm{LCM \: => \: 2 \: × \: 2 \: × \: 3 × \: 3 \: × \: 5}$

$\large\underline\mathrm{HCF \: => \: 12 \: × \: 5 \: × \: 3 \: = \: 180}$

$\large\underline\mathrm{LCM \: => \: 180 \: × \: 8 \: = \: 1440}$

Now,

Expressing 180 in the form of 13m - 3.

$\implies$ 13m - 3 = 180

$\implies$ 13m = 183

$\implies$ m = 183/13

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{The \: value \: of \: m \: is \: 183/13}$

$\large\underline\mathrm{LCM \: × \: HCF \: = \: products \: of \: two \: numbers}$

$\implies$ 180 × 1440 = 180 × 1440

$\implies$ 259200 = 259200

$\large\underline\mathrm{LHS \: = \: RHS}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$