Một số tự nhiên được viết bởi 2020 chữ số 7. Hỏi phải cộng thêm vào số đó ít nhất bao nhiêu đơn vị để được một số chia hết cho 21?

Phương pháp giải

Số tự nhiên chia hết cho 21 thì số đó chia hết cho 3 và chia hết cho 7.

Lời giải của GV ufaindo.xyz

Gọi a là số cộng thêm vào

Suy ra (777…..7777 + a) $ \vdots $ 3 và (777..…777 + a) $ \vdots $ 7 Có 777…..777 $ \vdots $ 7 nên a $ \vdots $ 7 Lại có 777…..777 có tổng các chữ số là 2020 x 7 = 14140 Mà 14140 chia 3 dư 1 nên 777 ….777 chia 3 dư 1. Để (777….777 + a) chia hết cho 3 thì a chia 3 dư 2 Suy ra a = 2 ; 5 ; 8 ; 11 ; 14 ; … Mà a chia hết cho 7 nên a = 14. Vậy phải cộng thêm vào số đó 14 đơn vị để được một số chia hết cho 21.

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