What is the GCF of 52 and 78? Explain the method you used to find it.
52 = 26*2
78 = 26*3
Clearly the greatest common factor is 26
Okay, thank you!
When was he or she being rude ?
Ah, the GCF of 52 and 78, you say? Well, let me put on my mathematical clown shoes and juggle those numbers for you!
To find the Greatest Common Factor (GCF), we can use a method called factoring. We start by breaking down both 52 and 78 into their prime factors. Now, prime factors are like the hippest and trendiest numbers in town, so we want to find all the cool kids that hang out in their factor group.
Let's start with 52. We can divide it by 2 to get 26. And guess what, 26 is also divisible by 2, it becomes 13. Now we have 13 left, which happens to be a prime number. So the prime factorization of 52 is 2 x 2 x 13.
Now let's move to 78. Dividing it by 2, we get 39. And hey, 39 can be divided by 3, giving us 13. Looks like that cool kid 13 is showing up again! So the prime factorization of 78 is 2 x 3 x 13.
Now, we need to find the common factors between these two prime factorizations. We see that the only prime factor they share is 13. So the GCF of 52 and 78 is just 13!
And there you have it, my friend! The mathematician clown has spoken, and the GCF between 52 and 78 is 13.
To find the greatest common factor (GCF) of 52 and 78, we can use the method of prime factorization.
Step 1: Prime factorize both numbers.
- The prime factorization of 52 is 2^2 × 13.
- The prime factorization of 78 is 2 × 3 × 13.
Step 2: Identify the common prime factors.
Both 52 and 78 have the prime factor 13 in common. However, they do not have any other common prime factors.
Step 3: Multiply the common prime factor(s).
The GCF is found by multiplying the common prime factors, which in this case is 13.
Therefore, the GCF of 52 and 78 is 13.
Another method for finding the GCF is using the Euclidean algorithm. This algorithm involves dividing the two numbers repeatedly until the remainder becomes zero. The GCF is the last non-zero remainder.
Step 1: Divide 78 by 52. The remainder is 26.
Step 2: Divide 52 by 26. The remainder is 0.
Since the remainder is now zero, the GCF is the last non-zero remainder, which in this case is 26.
However, since the prime factorization method is faster and more efficient for small numbers, it is generally preferred.