What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The largest number that divides 245 and 1029, leaving the remainder 5 in each case is 16. To reach this number, we can use two methods. The first method is to subtract 5 from 245 and 1029 and then take their HCF. Another way to solve this question is by using the prime factorization method. We have demonstrated both methods below.

Table of content

1. Largest number that divides 245 and 1029 and Leaves Remainder 5 in each case
2. By Prime Factorization Method
3. What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

Largest number that divides 245 and 1029 and Leaves Remainder 5 in each case

The largest number, 16 will divide 254 and 1029 leaving 5 as a remainder in each case. To calculate this number, follow the solution provided below.

As the remainder for both 245 and 1029 will be 5, the first step is to subtract the remainder from these numbers.

245−5=240

1029−5=1024

The next step is to calculate the HCF of these newly derived numbers which are 240 and 1024.

Keeping this in mind, we will calculate the HDF in the following way:

1024=240×4+64

240=64×3+48

64=48×1+16

48=16×3+0

As is evident, the common number is 16 which is the H.C.F as well.

Thus, the largest number that divides 245 and 1029 leaving the remainder 5 in each case is 16.

By Prime Factorization Method

There is another method to calculate the largest number that divides 245 and 1029 leaving the remainder 5 in each case. For this, we will employ the prime factorization method. Let’s find out the prime factors of 240 and 1024 below.

240=2×2×2×2×3×5

1024=2×2×2×2×2×2×2×2×2×2

Taking the number of times 2 appears in these equations, the HCF(240,1024) will be –

2×2×2×2=16

Hence, 16 is the answer and the largest number that can divide 245 and 1029 to give 5 as a remainder in each case.

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