Find the greatest number which divides 285 and 1249 leaving remainders 9 & 7 respectively.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

138 is the greatest number divisible by 285 and 1249 leaving remainders 9 & 7 respectively. We can find this answer by calculating the highest common factor or HCF of the numbers we will derive after subtracting remainders from the original numbers. It is a step-by-step method that helps in finding the required divisor.

Greatest Number that Divides 285 and 1249 with Remainders 9 & 7

To find the greatest number that divides are 285 and 1249 leaving remainders are 9 and 7, we will first subtract the numbers from their respective remainders.

285 – 9 = 276

1249 – 7 = 1242

Now, by using the factorization method, we will find the HCF of 276 and 1242 as it will give us our answer.

HCF by Prime Factorization Method

The full form of HCF is highest common factor. When calculating HCF by the prime factorization method, we take the factors of the numbers provided to us in the following way.

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

Thus, HCF (276, 1242)= 138

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

Summary:

Find the greatest number which divides 285 and 1249 leaving remainders 9 & 7 respectively.

The greatest number which divides 285 and 1249 while leaving 9 and 7 as remainders is 138. To calculate this answer, one must first find the numbers that are divisible by the greatest number by subtracting the remainder from the original numbers. Then, by finding HCF we will get our answer.

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