Question

If remainder of (5+1)(5+3)(5+4)divided by 5 is a natural number ,then find it.

Answer 1

Easy way... Use congruences:

(5m+1)(5m+3)(5m+4) ≡ (1)(3)(4) = 12 ≡ 2 (mod 5)

Harder way...  Expand:

(5m+1)(5m+3)(5m+4)

= 5³m³ + 5²m²(1+3+4) + 5m((1)(3)+(1)(4)+(3)(4)) + (1)(3)(4)

= 5³m³ + 5²m²×8 + 5m×19 + 12

= 5 × ( 5²m³ + 5m²×8 + m×19 + 2 ) + 2

[ last step used 12 = 5 × 2 + 2 ]

So when (5m+1)(5m+3)(5m+4) is divided by 5, the remainder is 2.

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Answer 2

Step-by-step explanation:

आई कांट अंडरस्टैंड आस्क एनी अदर क्वेश्चंस