if sum of two numbers is 1215 and their HCF is 81, then the possible number of pairsof such numbers are

### Asked by avanupama.srinath | 15th Sep, 2021, 05:07: PM

###
It is given that the sum of two numbers is 1215 and their H.C.F is 81

Since the H.C.F of two numbers is 81, the two numbers are 81x and 81y.

Now, 81x + 81y = 1215 [Sum of two numbers is 1215]

or, 81 (x + y) = 1215

or, (x + y) = 15

Such pairs of numbers whose sum is 15 are (1, 14), (2, 13), (4, 11), (7, 8)

For x = 1, y = 14; in this case the numbers are 1 × 81 = 81 and 14 × 81 = 1134

For x = 2, y = 13; in this case the numbers are 2 × 81 = 162 and 13 × 81 = 1053

For x = 4, y = 11; in this case the numbers are 4 × 81 = 324 and 11 × 81 = 891

For x = 7, y = 8; in this case the numbers are 7 × 81 = 567 and 8 × 81 = 648

Hence four pairs are possible.

It is given that the sum of two numbers is 1215 and their H.C.F is 81

Since the H.C.F of two numbers is 81, the two numbers are 81x and 81y.

Now, 81x + 81y = 1215 [Sum of two numbers is 1215]

or, 81 (x + y) = 1215

or, (x + y) = 15

Such pairs of numbers whose sum is 15 are (1, 14), (2, 13), (4, 11), (7, 8)

For x = 1, y = 14; in this case the numbers are 1 × 81 = 81 and 14 × 81 = 1134

For x = 2, y = 13; in this case the numbers are 2 × 81 = 162 and 13 × 81 = 1053

For x = 4, y = 11; in this case the numbers are 4 × 81 = 324 and 11 × 81 = 891

For x = 7, y = 8; in this case the numbers are 7 × 81 = 567 and 8 × 81 = 648

Hence four pairs are possible.

### Answered by Renu Varma | 15th Sep, 2021, 10:16: PM

## Application Videos

## Concept Videos

- Q (1) The HCF of 96 and 404 is .......
- P and q are two consecutive even natural number 72 then HCF of P and q is
- If xy=4320 and LCM(x,y)=360 then find the HCF(x,y)
- The traffic lights at three different roads crossing change after every 48 seconds ,72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m . Then at what time will they again change simultaneously
- In the 10th question of 1b from rs aggarwal .why did we subtract 7 from lcm
- find the HCF & LCM of 96 & 404
- find the smallest no.when no.30,40,and 60,divided and leaves remainder 7
- express each number as a product of it prime 1771 AND 3825
- What will be the product of HCF and LCM of the smallest prime number and the smallest composite number?

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change