Question

2. Find the greatest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15
respectively.
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Answer 1

$\huge\sf\pink{Answer}$

☞ So the number is 17

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ We divide 398,435 and 542 by a number leaving a remainder of 7,11 and 15

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ The number by which it is divided?

$\rule{110}1$

$\huge\sf\purple{Steps}$

So if we subtract the remainder from the number then the number should be divisible by the number by which they are divided.

➢ 398 - 7 = 391

➢ 436 - 11 = 425

➢ 542 - 15 = 527

So the HCF(405,447,527)

➝ 391 = 17 × 23

➝ 425 = 5 × 5 × 17

➝ 527 = 17 × 31

So the $\sf\orange {HCF(405,447,527) = 17}$

$\rule{170}3$

Answer 2

Answer = 17

Given :

To divide 398,435 and 542 by a number leaving a remainder of 7,11 and 15

To find :

• Number which is divided ?

Solution :

We need Deduct the remainders from numbers .

then

We wil get,

$\sf 398 \: − \: 7 \: = \: 391 \\ \sf 436 \: − \: 11 \: = \: 425 \\ \sf 542 \: − \: 15 \: = \: 527$

H.C.F of these numbers will be the largest possible number that divides into 398,436,542 leaving respective remainders .

$\sf391=17×23 \\ \sf425=17×52 \\\sf527=17×31$

∴ H.C.F( 391,425,527 ) = 17