Question

5. Find the greatest number that will divide 1025, 1299 and 1575 leaving remainders 5, 7 and 11 respectively.

Answer 1

$\huge\mathfrak{Answer:}$

Given:

• We have been given three numbers, 1025, 1299 and 1575.

To Find:

• We need to find the greatest number that will divide 1025, 1299 and 1575 leaving remainders 5, 7 and 11 respectively.

Solution:

We have been given three numbers, 1025, 1299 and 1575.

Inorder to find the greatest number that will divide 1025, 1299 and 1575 leaving remainders 5, 7 and 11 respectively, we need to subtract 5, 7 and 11 from 1025, 1299 and 1575 respectively and then find their HCF.

1025 - 5 = 1020

1299 - 7 = 1292

1575 - 11 = 1564

Now, we need to find the HCF of 1020, 1292 and 1564.

We can find the HCF of 1020, 1292 and 1564 by prime factorisation method.

[Shown in attachment]

Therefore, HCF of 1020, 1292 and 1564 is:

2 × 2 × 17

= 4 × 17

= 68

Hence, the required number is 68.

Answer 2

Answer:

68

Step-by-step explanation:

Given:

We have been given three numbers, 1025, 1299 and 1575.

To Find:

We need to find the greatest number that will divide 1025, 1299 and 1575 leaving remainders 5, 7 and 11 respectively.

Solution:

We have been given three numbers, 1025, 1299 and 1575.

Inorder to find the greatest number that will divide 1025, 1299 and 1575 leaving remainders 5, 7 and 11 respectively, we need to subtract 5, 7 and 11 from 1025, 1299 and 1575 respectively and then find their HCF.

1025 - 5 = 1020

1299 - 7 = 1292

1575 - 11 = 1564

Now, we need to find the HCF of 1020, 1292 and 1564.

We can find the HCF of 1020, 1292 and 1564 by prime factorisation method.

[Shown in attachment]

Therefore, HCF of 1020, 1292 and 1564 is:

2 × 2 × 17

= 4 × 17

= 68

Hence, the required number is 68.