Find the Greatest Common Factor of: 50, 78, 112. Make sure to show and/or explain all your work. (2 points)
To find the greatest common factor of 50, 78, and 112, we can use the prime factorization method.
First, we will find the prime factorization for each number:
- Prime factorization of 50: 2 * 5 * 5
- Prime factorization of 78: 2 * 3 * 13
- Prime factorization of 112: 2 * 2 * 2 * 2 * 7
Next, we will identify the common prime factors among the three numbers: 2.
Finally, we find the product of the common prime factors: 2 * 2 = 4.
Therefore, the greatest common factor of 50, 78, and 112 is 4.
To find the greatest common factor (GCF) of 50, 78, and 112, we can use either the prime factorization method or the division method.
Method 1: Prime Factorization
1. Prime factorize each number:
- 50 = 2 * 5 * 5
- 78 = 2 * 3 * 13
- 112 = 2 * 2 * 2 * 2 * 7
2. Identify the common prime factors among the three numbers. The common prime factors are 2 and 2.
3. Multiply the common prime factors to find the GCF:
GCF = 2 * 2 = 4
Method 2: Division
1. Start with one of the three numbers, let's say 50.
2. Divide 50 by 2, which gives us 25. (50 ÷ 2 = 25)
3. Divide 25 by 5, which gives us 5. (25 ÷ 5 = 5)
4. Repeat the process for each number, 78 and 112.
- For 78:
- Divide 78 by 2, which gives us 39. (78 ÷ 2 = 39)
- Divide 39 by 3, which gives us 13. (39 ÷ 3 = 13)
- For 112:
- Divide 112 by 2, which gives us 56. (112 ÷ 2 = 56)
- Divide 56 by 2, which gives us 28. (56 ÷ 2 = 28)
- Divide 28 by 2, which gives us 14. (28 ÷ 2 = 14)
- Divide 14 by 2, which gives us 7. (14 ÷ 2 = 7)
5. Identify the common factors at each step. The common factors are 2 and 13.
6. Multiply the common factors to find the GCF:
GCF = 2 * 13 = 26
So, the greatest common factor (GCF) of 50, 78, and 112 is 4 (using the prime factorization method) or 26 (using the division method).