What is the GCF of 360 and 252? PAR 6.2
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1 point
42
36
72
14
The GCF of 360 and 252 is 36.
To find the greatest common factor (GCF) of 360 and 252, we can look for the largest number that divides both of them evenly. Here is one way to find the GCF:
Step 1: Make a list of all the factors of 360.
The factors of 360 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
Step 2: Make a list of all the factors of 252.
The factors of 252 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
Step 3: Find the common factors from both lists.
The common factors of 360 and 252 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 4: Identify the largest common factor as the GCF.
The largest common factor of 360 and 252 is 36.
Therefore, the GCF of 360 and 252 is 36.
To find the greatest common factor (GCF) of 360 and 252, you can use a method called prime factorization.
1. Start by finding the prime factorization of both numbers:
- The prime factorization of 360 is: 2^3 × 3^2 × 5
- The prime factorization of 252 is: 2^2 × 3^2 × 7
2. Identify the common prime factors in both numbers. In this case, the common prime factors are 2^2 and 3^2.
3. Multiply the common prime factors together:
- 2^2 × 3^2 = 4 × 9 = 36
Therefore, the GCF of 360 and 252 is 36.
So the answer is 36.