Cho số 222...222 (2015 chữ số 2). Hỏi cần thêm vào ít nhất bao nhiêu đơn vị để được số chia hết cho 55?

Phương pháp giải

Số chia hết cho 55 thì số đó chia hết cho 5 và 11.

Lời giải của GV ufaindo.xyz

Gọi a là số cộng thêm vào

Suy ra (222…..222 + a) $ \vdots $ 5 và (222….222 + a) $ \vdots $ 11 Có 222…..222 chia 5 dư 2 nên a chia 5 dư 3 Lại có 222…..222 chia 11 dư 2 nên a chia 11 dư 9 Suy ra a = 9 ; 20 ; 31 ; 42 ; 53 ; … Mà a chia 5 dư 3 nên a = 53 Vậy phải cộng thêm vào số đó 53 đơn vị để được một số chia hết cho 55.

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