Find the prime factorization of each number,330
2.Find two factors of 28 with a sum of 11.7*4=28 =7+4=11
3.Find the greatest common factor for each of the following groups of numbers 36, 72, and 144 answer36, 72, and 144
1. prime factorization of 330
Find any prime factor (for example 2,3 or 5), and divide 330 by the factor. Repeat the same for the quotient. Enumerate all the prime factors you have used.
2. Correct
3. The GCF (greatest common factor) is a single number that divides two or more numbers without remainders.
For groups of numbers that represent multiples of one over the other, the GCF is the smallest number. For example, the GCF for 15,30,90 is 15, since 30 is a multiple of 15, and 90 is a multiple of 30.
1. To find the prime factorization of a number, such as 330, you need to break it down into its prime factors. Start by dividing the number by the smallest prime number, which is 2.
330 ÷ 2 = 165
Now divide the result, 165, by the next smallest prime number, which is 3.
165 ÷ 3 = 55
Again, divide the result, 55, by the next smallest prime number, which is also 5.
55 ÷ 5 = 11
Now we have reached a prime number, 11. Since it cannot be divided further, the prime factorization of 330 is 2 × 3 × 5 × 11.
Answer: The prime factorization of 330 is 2 × 3 × 5 × 11.
2. To find two factors of 28 with a sum of 11, one way is to manually go through the factors of 28 and check if any two numbers add up to 11. However, a quicker way is to list all the factors:
1, 2, 4, 7, 14, 28
Based on the list, we can see that 7 and 4 add up to 11.
Answer: Two factors of 28 with a sum of 11 are 7 and 4.
3. To find the greatest common factor (GCF) of the given numbers - 36, 72, and 144 - you need to find the largest number that divides evenly into all of them.
Step 1: Find the prime factorization of each number:
36 = 2^2 × 3^2
72 = 2^3 × 3^2
144 = 2^4 × 3^2
Step 2: Identify the common prime factors of all the numbers and take the lowest power of each common factor:
2^2 × 3^2
Step 3: Multiply the common prime factors:
2^2 × 3^2 = 4 × 9 = 36
Answer: The greatest common factor for 36, 72, and 144 is 36.