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Giải Bài 2.35 trang 39 sách bài tập Toán 6 Kết nối tri thức với cuộc sống

Hãy tìm ước chung lớn nhất rồi tìm ước chung của các số sau: a) 72 và 90; b) 200; 245 và 125.

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Đề bài

𒉰Hãy tìm ước chung lớn nhất rồi tìm ước chung của các số sau:

a) 72 và 90;

b) 200; 245 và 125.

Phương pháp giải - Xem chi tiết

*Các bước tìm ƯCLN của hai hay nhiều số lớn hơn 1: - Phân tích mỗi số ra thừa số nguyên tố - Chọn ra các thừa số nguyên tố chung - Lập tích các thừa số đã chọn, mỗi thừa số lấy với số mũ nhỏ nhất. Tích đó là ƯCLN phải tìm. *Ước của ƯCLN là ước chung

Lời giải chi tiết

a)+ Phân tích các số 72 và 90 ra thừa số nguyên tố:

72 = 23.32

90 = 2.32.5

+ Các thừa số nguyên tố chung là: 2 và 3.+ Số mũ nhỏ nhất của 2 là 1, số mũ nhỏ nhất của 3 là 2.

Khi đó:  ƯCLN(72; 90) = 2. 32 = 18.

Ta được ƯC(72; 90) = Ư(18) = {1; 2; 3; 6; 9; 18}Vậy ƯCLN(72; 90) = 18 và ƯC(72; 90) = {1; 2; 3; 6; 9; 18}.b) Phân tích các số 200; 245 và 125 ra thừa số nguyên tố:

200 = 23.52 

245 = 5.72     

125 = 53

+Thừa số nguyên tố chung là: 5.+Số mũ nhỏ nhất của 5 là 1 Khi đó ƯCLN(200; 245; 125) = 5.Ta được ƯC(200; 245; 125) = Ư(5) = {1; 5}Vậy ƯCLN(200; 245; 125) = 5 và ƯC(200; 245; 125) = {1; 5}.

 Lời giải hay

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