Find the GCF of the following set of numbers 260, 80, 50
The correct answer and explanation is:
The greatest common factor (GCF) of 260, 80, and 50 is 10.
Explanation:
To find the GCF, also known as the greatest common divisor (GCD), follow these steps:
- Find the prime factorization of each number:
- 260: Divide by 2 (the smallest prime number):
260 ÷ 2 = 130
130 ÷ 2 = 65
65 ÷ 5 = 13 (which is prime)
Therefore, the prime factorization of 260 is: 260=22×5×13260 = 2^2 \times 5 \times 13 - 80: Divide by 2:
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5 (which is prime)
Therefore, the prime factorization of 80 is: 80=24×580 = 2^4 \times 5 - 50: Divide by 2 and 5:
50 ÷ 2 = 25
25 ÷ 5 = 5
Therefore, the prime factorization of 50 is: 50=2×5250 = 2 \times 5^2
- 260: Divide by 2 (the smallest prime number):
- Identify the common prime factors:
From the prime factorizations, the common prime factors are 2 and 5. - Choose the smallest power of each common prime factor:
- For 2, the smallest power is 212^1 (since 260 has 222^2, 80 has 242^4, and 50 has 212^1).
- For 5, the smallest power is 515^1 (since all three numbers contain 515^1 or higher powers).
- Multiply the smallest powers of the common factors: GCF=21×51=2×5=10GCF = 2^1 \times 5^1 = 2 \times 5 = 10
Thus, the GCF of 260, 80, and 50 is 10. This is the largest number that divides all three numbers without leaving a remainder.