find largest number which divides 2053 and 967 and leaves remainder 5 and 7 respectively

### Asked by arajeevshashank | 12th Mar, 2020, 08:41: AM

Expert Answer:

###
2053 - 5 = 2048 and 967 - 7 = 960
Prime factorisation of 2048 and 960 are as follows,
2048 = 2^{11} and 960 = 2^{6 }× 3 × 5
HCF(2048, 960) = 2^{6} =64
Therefore, the largest number which divides 2053 and 967 and leaves remainder 5 and 7 respectively is **64**.

^{11}and 960 = 2

^{6 }× 3 × 5

^{6}=64

**64**.

### Answered by Yasmeen Khan | 12th Mar, 2020, 11:03: AM

## Related Videos

- ) Use Euclid's division lemma to find HCF of 4052 and 12576.
- is √2 a rational number
- Find the h c f of 75 and 243
- show that any positive odd integer is of the form 6q +1 or 6q+3 or 6q+5
- If two positive integers a and b are written as a=(x^3) * (y^2) and b=x * ( y^3), x and y are prime numbers , then HCF (a,b) is ?
- The least number that is divisible by all the numbers from 1 to 10 (both inclusive ) is ?
- 10. If 3 is the least prime factor of p and 5 is the least prime factor of q, then the least prime factor of p+q __________.
- Find the greatest number digit of 6 digit Exactly divisible by 24 ,15 and 36?
- The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: _____ Greatest number of 4-digits is 9999. To find the LCM of 15, 25, 40 and 75. 15 = 3 × 5 25 = 5 × 5 40 = 2 × 2 × 2 × 5 75 = 3 × 5 × 5 L.C.M. of 15, 25, 40 and 75 = 2 × 2 × 2 × 3 × 5 × 5 = 600. On dividing 9999 by 600, the remainder is 399. Required number (9999 - 399) = 9600. PLEASE GO THROUGH THE ABOVE SOLUTION AND EXPLAIN ME THE FOLLOWING POINTS : Why we took LCM OF 15 , 25 , 40 , 75(REASON IN BREIF ) WHY WE DIVIDED THE LCM (600) AND 9999. WHY WE SUBTRACTED THE REMAINDER WHY SUBTRACTING THE REMAINDER GIVES US THE ANSWER. HOPE YOU EXPLAIN IN BREIF REGARDS, ANAS

### 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