The simplest form of a factor tree for the number 1225 involves breaking it down into its prime factors. Here’s a step-by-step explanation of how to create the factor tree and find the simplest form:
Step 1: Determine if 1225 is divisible by smaller prime numbers
First, let’s check if 1225 is divisible by the smallest prime numbers:
- 1225 is odd, so it is not divisible by 2.
- Add the digits of 1225 (1 + 2 + 2 + 5 = 10) to check divisibility by 3. Since 10 is not divisible by 3, neither is 1225.
- Since it ends in 5, 1225 is divisible by 5. Performing the division:
1225 ÷ 5 = 245
Step 2: Factor 245
Next, we need to factor 245:
- Again, check for divisibility by 5:
245 ÷ 5 = 49
Step 3: Factor 49
Now we factor 49:
- 49 is not divisible by 5, but it is equal to 7 × 7. Hence:
49 = 7 × 7
Step 4: Compile all factors
Now we can summarize all the factors we’ve found:
- 1225 = 5 × 245 = 5 × 5 × 49 = 5 × 5 × 7 × 7
Step 5: Present the prime factorization
The prime factorization of 1225 is:
1225 = 5² × 7²
Conclusion
The simplest form of the factor tree for 1225 shows that the number can be expressed as the product of its prime factors, which are 5 and 7. Therefore, the final prime factorization is:
5² × 7²
When you see the factor tree drawn out, it will highlight the hierarchical structure of these factors visually, but the key takeaway here is that 5 squared and 7 squared represent the simplest form of 1225 when factored into primes.