What is the greatest common factor for the numbers 24, 36, and 60?

Question

UpStudy AI · Accepted Answer

To find the **Greatest Common Factor (GCF)** of the numbers **24**, **36**, and **60**, you can follow these steps:

### Step 1: Prime Factorization
Break down each number into its prime factors.

- **24**
  - $$24 = 2 \times 12$$
  - $$12 = 2 \times 6$$
  - $$6 = 2 \times 3$$
  - **Prime Factors:** $$2^3 \times 3^1$$

- **36**
  - $$36 = 2 \times 18$$
  - $$18 = 2 \times 9$$
  - $$9 = 3 \times 3$$
  - **Prime Factors:** $$2^2 \times 3^2$$

- **60**
  - $$60 = 2 \times 30$$
  - $$30 = 2 \times 15$$
  - $$15 = 3 \times 5$$
  - **Prime Factors:** $$2^2 \times 3^1 \times 5^1$$

### Step 2: Identify Common Prime Factors
Look for the prime factors common to all three numbers.

- **Common Prime Factors:** $$2$$ and $$3$$

### Step 3: Determine the Lowest Powers
For each common prime factor, take the lowest exponent present in the factorizations.

- For **2**: The lowest power is $$2^2$$ (from 36 and 60).
- For **3**: The lowest power is $$3^1$$ (from 24 and 60).

### Step 4: Calculate the GCF
Multiply these together to get the GCF.

$$
\text{GCF} = 2^2 \times 3^1 = 4 \times 3 = 12
$$

**Therefore, the greatest common factor of 24, 36, and 60 is **12**.
The greatest common factor of 24, 36, and 60 is 12.

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