Question

If the HCF of 408 and 1032 is expressible in the form 1032p – 408 × 5 find p.

Answer 1

Step-by-step explanation:

Given :-

The HCF of 408 and 1032 is expressible in the

form 1032p – 408 × 5 .

To find:-

If the HCF of 408 and 1032 is expressible

in theform 1032p – 408 × 5 find the

value of p ?

Solution:-

Given numbers are 408 and 1032

408 can be written as

408=2×2×2×3×17=2^3 × 3^1 ×17^1

1032 can be written as

1032 = 2×2×2×3×43=2^3 ×3^1 ×43^1

HCF of 408 and 1032 = 2^3 × 3^1 =8×3 =24

According to the given problem

The HCF of 408 and 1032 is expressible in the

form of 1032p – 408 × 5

=>1032 p -408×5 = 24

=>1032p - 2040 = 24

=>1032p = 24+2040

=>1032p = 2064

=>p=2064/1032

=>p=2

Therefore, p=2

Answer:-

The value of p for the given problem is 2

Check:-

If p = 2 then 1032p – 408 × 5

=>1032(2) -408×5

=>2064 - 2040

=>24

1032p – 408 × 5 = 24

Verified the given relation

Answer 2

Given,

• The HCF of 408 and 1032 is expressible in the form 1032P – 408 × 5

To Find,

• The Value Of P.

Solution,

The Prime Factorisation Of 408

= 2 × 2 × 2 × 3 × 17 × 1

= 2³ × 3¹ × 17¹

The Prime Factorisation Of 1032

= 2 × 2 × 2 × 2 × 3 × 3 × 7 × 1

= 2⁴ × 3² × 7¹

The Common Factor = 2³ , 3¹

The HCF = 2³ × 3

= 8 × 3

= 24

The HCF = 1032P – 408× 5

24 = 1032P – 2040

24 + 2040 = 1032P

2064 = 1032P

2064/1032 = P

2 = P

Required Answer,

P = 2