Question

Use Euclid's division algorithm to find the HCF (a,b) of the following numbers 'a' and 'b' and hence find
integers m and n such that HCF(a,b)=am+bn
j) 256,1024
answer is (-3,1)
but tell me the steps of how to arrive at the answer...pls write the answer on a page ​

Answer 1

Step-by-step explanation:

Given -

• Numbers 256, 1024

To Find -

• HCF(a,b)
• Find integer m and n

Now,

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Now,

HCF(256,1024) = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

→ 256

Hence,

HCF(256,1024) is 256.

Now,

• HCF(a,b) = am + bn

→ HCF(256,1024) = 256m + 1024n

→ 256 = 256m + 1024n

→ 256 = 256(-3) + 1024(1)

→ 256 = 1024 - 768

→ 256 = 256

LHS = RHS

Hence,

The value of m is -3 and n is 1.

Answer 2

$\bold{ANSWER}$

$\red{ \ Given :-}$

Numbers 256, 1024

$\red{ \ To \ Find:-}$

• HCF(a,b)

• HCF(a,b)Find integer m and n

$\red{ \ Now,}$

• 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

• 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 21024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

$\red{ \ Now,}$

HCF(256,1024) = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

→ 256

$\red{ \ Hence,}$

HCF(256,1024) is 256.

$\red{ \ Now,}$

HCF(a,b) = am + bn

→ HCF(256,1024) = 256m + 1024n

→ 256 = 256m + 1024n

→ 256 = 256(-3) + 1024(1)

→ 256 = 1024 - 768

→ 256 = 256

$\pink{ \ LHS \ = \ RHS}$

$\pink{ \ Hence,}$

The value of m is -3 and n is 1.