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Đáp án:

Giải thích các bước giải:

 a, 100 chia hết cho x

     120 chia hết cho x

     160 chia hết cho x

     x lớn nhất

⇒ x ∈ ƯCLN ( 100 ; 120 ; 160 )

Ta có

    100 = 2² . 5²

    120 = 2³ . 3 . 5

    160 = 2^5 . 5

ƯCLN ( 100 ; 120 ; 160 ) = 2² . 5 = 20

vậy x = 20

Đáp án:

Giải thích các bước giải:

Find the natural number xxx such that: 100:x;120:x;160:x vaˋ x lớn nhaˆˊt100 : x ; 120 : x ; 160 : x \text{ và } x \text{ lớn nhất}100:x;120:x;160:x vaˋ x lớn nhaˆˊt

To solve this, xxx should be the greatest common divisor (GCD) of 100, 120, and 160.

Calculating the GCD: GCD(100,120,160)=20\text{GCD}(100, 120, 160) = 20GCD(100,120,160)=20

So, x=20x = 20x=20.

Problem 2

Find the natural number xxx such that: x∈UC(98,56) vaˋ x lớn nhaˆˊtx \in \text{UC}(98, 56) \text{ và } x \text{ lớn nhất}x∈UC(98,56) vaˋ x lớn nhaˆˊt

UC(98, 56) means the common divisors of 98 and 56. The largest common divisor is the GCD of 98 and 56.

Calculating the GCD: GCD(98,56)=14\text{GCD}(98, 56) = 14GCD(98,56)=14

So, x=14x = 14x=14.

Problem 3

Find the natural number xxx such that: x∈Ư(48) vaˋ 5<x≤12x \in \text{Ư}(48) \text{ và } 5 < x \leq 12x∈Ư(48) vaˋ 5<x≤12

Ư(48) means the divisors of 48. The divisors of 48 are: 1,2,3,4,6,8,12,16,24,481, 2, 3, 4, 6, 8, 12, 16, 24, 481,2,3,4,6,8,12,16,24,48

Among these, the values of xxx that satisfy 5<x≤125 < x \leq 125<x≤12 are: 6,8,126, 8, 126,8,12

Problem 4

Find the natural number xxx such that: x:10;x:18 vaˋ 250<x<350x : 10 ; x : 18 \text{ và } 250 < x < 350x:10;x:18 vaˋ 250<x<350

For xxx to be divisible by both 10 and 18, it must be a multiple of their least common multiple (LCM).

Calculating the LCM: LCM(10,18)=90\text{LCM}(10, 18) = 90LCM(10,18)=90

The multiples of 90 in the range 250 to 350 are: 270 and 360270 \text{ and } 360270 and 360

So, x=270x = 270x=270 (since 360 is outside the range).

Problem 5

Find the natural number xxx such that: x:7;x:5;x:2 vaˋ x nhỏ nhaˆˊtx : 7 ; x : 5 ; x : 2 \text{ và } x \text{ nhỏ nhất}x:7;x:5;x:2 vaˋ x nhỏ nhaˆˊt

For xxx to be divisible by 7, 5, and 2, it must be a multiple of their least common multiple (LCM).

Calculating the LCM: LCM(7,5,2)=70\text{LCM}(7, 5, 2) = 70LCM(7,5,2)=70

So, x=70x = 70x=70.

Summary

1. x=20x = 20x=20
2. x=14x = 14x=14
3. x=6,8,12x = 6, 8, 12x=6,8,12
4. x=270x = 270x=270
5. x=70x = 70x=70