Question

Which is the largest number which when devides 650, 775, 1250 leaves the same remainder?​

Answer 1

The greatest number which when divides 253,568 and 813 leaves the same remainder each time
→ HCF of (568−253),(813−568),(813−253)= HCF of 315,245 and 560

Prime factorisation of 315,245 and 560 is,

315=3×3×5×7
245=7×7×5
560=2×2×2×2×5×7

Therefore HCF of 315,245 and 560 is 5×7=35.

The greatest number which when divides 253,568 and 813 leaves the same remainder each time is 35 and the remainder obtained in each case is 8.