Let's find the other number given that the Highest Common Factor (HCF) is 5, the Least Common Multiple (LCM) is 46,905, and one of the numbers is 265.
To solve this, we'll use the relationship between the HCF, LCM, and the two numbers involved in the equation:
[tex]\[ \text{HCF} \times \text{LCM} = \text{number1} \times \text{number2} \][/tex]
Given:
- HCF = 5
- LCM = 46,905
- number1 = 265
We need to find number2. Rearrange the equation to solve for number2:
[tex]\[ \text{number2} = \frac{\text{HCF} \times \text{LCM}}{\text{number1}} \][/tex]
Substitute the known values into the equation:
[tex]\[ \text{number2} = \frac{5 \times 46,905}{265} \][/tex]
Calculate the numerator:
[tex]\[ 5 \times 46,905 = 234,525 \][/tex]
Then, divide by the denominator:
[tex]\[ \text{number2} = \frac{234,525}{265} \][/tex]
Carrying out the division:
[tex]\[ \text{number2} = 885 \][/tex]
So, the other number is 885.
