Write the ratio in simplest from :
`144:162`

Answer

To simplify the ratio \( 144:162 \), we can follow these steps:

### Step 1: Write the ratio as a fraction
We start by expressing the ratio \( 144:162 \) as a fraction:
\[ \frac{144}{162} \]

### Step 2: Find the greatest common divisor (GCD)
Next, we need to find the GCD of 144 and 162. We can do this by listing the factors or using the prime factorization method.

- The prime factorization of 144 is:
\[ 144 = 2^4 \times 3^2 \]
- The prime factorization of 162 is:
\[ 162 = 2^1 \times 3^4 \]

The GCD is found by taking the lowest power of each prime factor common to both numbers:
- For \( 2 \): the minimum power is \( 2^1 \)
- For \( 3 \): the minimum power is \( 3^2 \)

Thus, the GCD is:
\[ GCD = 2^1 \times 3^2 = 2 \times 9 = 18 \]

### Step 3: Divide both terms by the GCD
Now, we divide both the numerator and the denominator by the GCD (18):
\[ \frac{144 \div 18}{162 \div 18} = \frac{8}{9} \]

### Step 4: Write the simplified ratio
The simplified form of the ratio \( 144:162 \) is:
\[ 8:9 \]

### Final Answer
Thus, the ratio \( 144:162 \) in simplest form is \( 8:9 \).

---