Question

Find the largest number that will divide 280,351 and 449 leaving remainder 4, 3 and 5 respectively...

Answer 1

Step-by-step explanation:

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Answer 2

Largest number is 12.

Step-by-step explanation:

1. Here it is given number, which are

  First number $\mathbf{(N_{1})=280}$

  Second number $\mathbf{(N_{2})=351}$

  Third number $\mathbf{(N_{3})=449}$

2. After dividing with larger number, there are remainder

   First remainder $\mathbf{(R_{1})=4}$

   Second remainder $\mathbf{(R_{2})=3}$

   Third remainder $\mathbf{(R_{3})=5}$

3. Then larger number will be H.CF of $\mathbf{(N_{1}-R_{1})}$ ,$\mathbf{(N_{2}-R_{2})}$ and $\mathbf{(N_{3}-R_{3})}$

   Means

   H.C.F of (280-4),(351-3) and (449-5)

4. Again

   H.C.F of (276),(348) and (444) , which are

   276 = 2×2×3×23

   348 = 2×2×3×29

   444 = 2×2×3×37

   From above it is clear that

  H.C.F = 2×2×3= 12

5. Means 12 will be larger number which leave remainder 4,3 and 5 after dividing 280,351 and 449.