What is the greatest common factor of 30, 90, and 130?
ten times greatest common factor of 3, 9, 13
but they have no common factors
so we are stuck with ten
To find the greatest common factor (GCF) of 30, 90, and 130, we need to find the largest number that divides evenly into all three numbers.
Step 1: Find the factors of each number:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130.
Step 2: Identify the common factors:
The common factors of 30, 90, and 130 are 1, 2, 5, and 10.
Step 3: Determine the greatest common factor:
The greatest common factor of 30, 90, and 130 is 10.
Therefore, the GCF of 30, 90, and 130 is 10.
To find the greatest common factor (GCF) of three numbers, we can use the method of prime factorization. Let's find the prime factorization of each number and then determine the common factors.
Prime factorization of 30:
30 can be divided by 2, giving us 15.
15 can be divided by 3, giving us 5.
So, the prime factorization of 30 is 2 x 3 x 5.
Prime factorization of 90:
90 can be divided by 2, giving us 45.
45 can be divided by 3, giving us 15.
15 can be divided by 3, giving us 5.
So, the prime factorization of 90 is 2 x 3 x 3 x 5.
Prime factorization of 130:
130 can be divided by 2, giving us 65.
65 can be divided by 5, giving us 13.
So, the prime factorization of 130 is 2 x 5 x 13.
Now, let's find the common factors. We look for the factors that appear in all three prime factorizations.
The prime factors that are common to all three numbers are 2 and 5.
To find the GCF, we multiply the common prime factors together:
GCF = 2 x 5 = 10.
Therefore, the greatest common factor of 30, 90, and 130 is 10.