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Answer :
To find the highest common factor (HCF) of [tex]$114$[/tex] and [tex]$380$[/tex], we can follow these steps:
1. List all factors of [tex]$114$[/tex]. These are the numbers that divide [tex]$114$[/tex] evenly:
[tex]$$1,\; 2,\; 3,\; 6,\; 19,\; 38,\; 57,\; 114.$$[/tex]
2. List all factors of [tex]$380$[/tex]. These are the numbers that divide [tex]$380$[/tex] evenly:
[tex]$$1,\; 2,\; 4,\; 5,\; 10,\; 19,\; 20,\; 38,\; 76,\; 95,\; 190,\; 380.$$[/tex]
3. Identify the common factors of [tex]$114$[/tex] and [tex]$380$[/tex], i.e., the factors that appear in both lists:
[tex]$$1,\; 2,\; 19,\; 38.$$[/tex]
4. The highest number among these common factors is the HCF:
[tex]$$\text{HCF} = 38.$$[/tex]
Thus, the highest common factor of [tex]$114$[/tex] and [tex]$380$[/tex] is [tex]$\boxed{38}$[/tex].
1. List all factors of [tex]$114$[/tex]. These are the numbers that divide [tex]$114$[/tex] evenly:
[tex]$$1,\; 2,\; 3,\; 6,\; 19,\; 38,\; 57,\; 114.$$[/tex]
2. List all factors of [tex]$380$[/tex]. These are the numbers that divide [tex]$380$[/tex] evenly:
[tex]$$1,\; 2,\; 4,\; 5,\; 10,\; 19,\; 20,\; 38,\; 76,\; 95,\; 190,\; 380.$$[/tex]
3. Identify the common factors of [tex]$114$[/tex] and [tex]$380$[/tex], i.e., the factors that appear in both lists:
[tex]$$1,\; 2,\; 19,\; 38.$$[/tex]
4. The highest number among these common factors is the HCF:
[tex]$$\text{HCF} = 38.$$[/tex]
Thus, the highest common factor of [tex]$114$[/tex] and [tex]$380$[/tex] is [tex]$\boxed{38}$[/tex].
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