Question

Find the largest number which divided 129 and 545, leaving remainders 3 and 5 respectively

Answer 1

to find the largest number which divides 129 and 545 leaving remainder 3 and 5 i.e. HCF.

Consider HCF be x.

In order to make 129 and 545 completely divisible by x, we need to deduct the remainder 3 and 5 from the cases.

126 =2× 3 x 3 x 7

540= 2×2×3×3 x 3 x 5

⇒ x = 2×3×3 = 18

∴ largest number which divides 126 and 540 leaving remainder 3 and 5 in case is 18.

Answer 2

Answer:

18

given,

two positive integers - 129 and 545.

to find,

the largest number which divided 129 and 545, leaving remainders 3 and 5 respectively

solution,

to find the largest number which divided 129 and 545, leaving remainders 3 and 5 respectively,

• step-1 : subtract the remainders from the given numbers.
• 129- 3= 126
• 545- 5 = 540
• step-2 : find the HCF of the resulting numbers by prime factorization.
• 126 = 2 x 3 x 3 x 7
• 540 = 2 x 2 x 3 x 3 x 3 x 5
• step-3:  look for common factors and multiply them. this is the required HCF.

      common factors = 2 x 3 x 3

       HCF=  2 x 3  x 3 = 18

therefore, 18 is the required response.

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