Find the largest number which divides 245 and 1037 leaving remainder 5 in each case

Given ⇒leaving remainder 5 in each case Concept ⇒ The largest number which divides Mand N, leaving remainder Pin each case ⇒ Subtract P from each number and then find out H.C.F of the numbers because here the largest number is required. ⇒ (M - P) and (N - P) ⇒ For finding H.C.F prime factorization is used Calculation ⇒ First number = 245 - 5 = 240 ⇒ Second number 1037 - 5 = 1032 ⇒ Factor of 240 = 2× 2× 2× 2× 3× 5 and ⇒ Factor of 1032 =2× 2× 2× 3× 43 ⇒ H.C.F of (240, 1032) =2× 2× 2× 3 = 24 ∴ H.C.F of (240, 1032) = 24

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. 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 thelargest 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, theHCF(240,1024) will be - 2×2×2×2=16 Hence, ...

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