Question

la) 2 and 108 (b) 399 and 437 (c) 594, 792 and 1848
Find the greatest number that divides 135, 245 and 385 leaving a remainder 5 in each case.
Find the greatest number that divides 398, 436 and 542 leaving remainders 7,11 and 15 respectively
105 and
арас
2. Using division method, tind the
(Hint: The required greatest number is the HCF of (135 – 5), (245 – 5) and (385​

Answer 1

Answer:

2 and 108 (b) 399 and 437 (c) 594, 792 and 1848

Find the greatest number that divides 135, 245 and 385 leaving a remainder 5 in each case.

Find the greatest number that divides 398, 436 and 542 leaving remainders 7,11 and 15 respectively

105 and

арас

2. Using division method, tind the

(Hint: The required greatest number is the HCF of (135 – 5), (245 – 5) and (385​

Step-by-step explanation:

To find the largest number which when divided 285 and 1249 leaving the remainder 9 and 7 respectively. First we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

SOLUTION :

Given numbers are 285 and 1249 and remainders are 9 and 7 respectively. Then new numbers after subtracting remainders are :

285 – 9 = 276

1249 – 7 = 1242.

The required number is HCF of 276 and 1242.

HCF by prime factorization method :

Prime factorization of 276 = 2×2×3×23 = 2² × 3¹ × 23¹

Prime factorization of 1242 = 2×3×3×3×23 = 2¹ × 3³ × 23¹

HCF of 276 and 1242 = 2¹ ×3¹×23¹

= 6 × 23 = 138

[HCF of two or more numbers =  product of the smallest power of each common prime factor involved in the numbers.]

HCF of 276 and 1242 is 138.

Hence, the required greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.

HOPE THIS WILL HELP YOU….

Answer 2

Given:

(1) 135, 245 and 385

(2) 398, 436 and 542

To find:

(1) Find the greatest number that divides 135, 245 and 385 leaving a remainder 5 in each case.

(2) Find the greatest number that divides 398, 436 and 542 leaving remainders 7,11 and 15 respectively.

Solution:

In order to find the number that divides the three numbers leaving a remainder, the following calculations are made.

(1)

First, 5 is subtracted from 135, 245 and 385. So, these numbers become 130, 240 and 380. Next, the H.C.F. (Highest Common Factor) of the three numbers is found. The H.C.F. is 5 and hence, it is the greatest number that divides 135, 245 and 385 leaving a remainder 5 in each case.

(2)

Similarly, 7, 11 and 15 must be subtracted from 398, 436 and 542, respectively. Then, the numbers become 391, 425 and 527. Now, the H.C.F. of these numbers is found which is 17.

Therefore,

(1) Find the greatest number that divides 135, 245 and 385 leaving a remainder 5 in each case is 5.

(2) Find the greatest number that divides 398, 436 and 542 leaving remainders 7,11 and 15 respectively is 17.