Hãy viết thêm hai chữ số vào bên phải và một chữ số vào bên trái số 54 để được số lớn nhất có năm chữ số thỏa mãn tính chất: chia số đó cho 4 dư 3, cho 5 dư 4 và cho 9 dư 8.

Phương pháp giải

- Dấu hiệu chia hết cho 5: Số có tận cùng bằng 0 hoặc 5 thì chia hết cho 5 - Dấu hiệu chia hết cho 4: số có hai chữ số tận cùng tạo thành số chia hết cho 4 thì chia hết cho 4 - Dấu hiệu chia hết cho 9: Số có tổng các chữ số chia hết cho 9 thì chia hết cho 9

Lời giải của GV ufaindo.xyz

Gọi chữ số viết thêm vào bên trái là a, bên phải là b. Số cần tìm có dạng $\overline {a54bc} $. Vì $\overline {a54bc} $ chia cho 4 dư 3, cho 5 dư 4 và cho 9 dư 8 Để $\overline {a54bc} $ chia cho 5 dư 4 thì c = 4 hoặc c = 9 Mặt khác $\overline {a54bc} $ là số lớn nhất nên c = 9. Thay vào ta được số $\overline {a54b9} $ Để $\overline {a54b9} $ chia 4 dư 3 thì $\overline {b9} $ chia 4 dư 3. Nên b = 3 ; 5 ; 7 ; 9 Vì $\overline {a54b9} $ lớn nhất nên b = 9. Thay vào ta được số $\overline {a5499} $ Để $\overline {a5499} $ chia cho 9 dư 8 thì (a + 5 + 4 + 9 + 9) – 8 chia hết cho 9. Suy ra a + 19 chia hết cho 9. Nên a = 8 Vậy số cần tìm là 85499.

Báo lỗi - Góp ý

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