Math / Numbers & Operations

QuestionWhat is the greatest common factor of 18 and 24 ?

Studdy Solution

STEP 1

1. The problem requires finding the greatest common factor (GCF) of the integers 18 and 24.
2. The GCF of two integers is the largest positive integer that divides both of them without leaving a remainder.
3. The Euclidean algorithm is an effective method for finding the GCF of two integers.

STEP 2

1. Identify the prime factorizations of 18 and 24.
2. Compare the prime factorizations to determine the common prime factors.
3. Multiply the common prime factors to find the greatest common factor.

STEP 3

Prime factorize 18.
$18 = 2 \times 3^2$

STEP 4

Prime factorize 24.
$24 = 2^3 \times 3$

STEP 5

Identify the common prime factors between 18 and 24.
The common prime factors are 2 and 3.

STEP 6

Determine the lowest power of each common prime factor.
For the prime number 2, the lowest power is $2^1$ . For the prime number 3, the lowest power is $3^1$ .

STEP 7

Multiply the lowest powers of common prime factors to find the GCF.
$\text{GCF} = 2^1 \times 3^1 = 2 \times 3 = 6$
The greatest common factor of 18 and 24 is 6.

Was this helpful?

QuestionWhat is the greatest common factor of 18 and 24 ?

Studdy Solution

STEP 1

1. The problem requires finding the greatest common factor (GCF) of the integers 18 and 24.
2. The GCF of two integers is the largest positive integer that divides both of them without leaving a remainder.
3. The Euclidean algorithm is an effective method for finding the GCF of two integers.

STEP 2

1. Identify the prime factorizations of 18 and 24.
2. Compare the prime factorizations to determine the common prime factors.
3. Multiply the common prime factors to find the greatest common factor.

STEP 3

Prime factorize 18.
$18 = 2 \times 3^2$

STEP 4

Prime factorize 24.
$24 = 2^3 \times 3$

STEP 5

Identify the common prime factors between 18 and 24.
The common prime factors are 2 and 3.

STEP 6

Determine the lowest power of each common prime factor.
For the prime number 2, the lowest power is $2^1$ . For the prime number 3, the lowest power is $3^1$ .

STEP 7

Multiply the lowest powers of common prime factors to find the GCF.
$\text{GCF} = 2^1 \times 3^1 = 2 \times 3 = 6$
The greatest common factor of 18 and 24 is 6.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhat is the greatest common factor of 18 and 24 ?

Studdy Solution

STEP 1

1. The problem requires finding the greatest common factor (GCF) of the integers 18 and 24.2. The GCF of two integers is the largest positive integer that divides both of them without leaving a remainder.3. The Euclidean algorithm is an effective method for finding the GCF of two integers.

STEP 2

1. Identify the prime factorizations of 18 and 24.2. Compare the prime factorizations to determine the common prime factors.3. Multiply the common prime factors to find the greatest common factor.

STEP 3

Prime factorize 18.18=2×32 18 = 2 \times 3^2 18=2×32

STEP 4

Prime factorize 24.24=23×3 24 = 2^3 \times 3 24=23×3

STEP 5

Identify the common prime factors between 18 and 24.The common prime factors are 2 and 3.

STEP 6

Determine the lowest power of each common prime factor.For the prime number 2, the lowest power is 212^121. For the prime number 3, the lowest power is 313^131.

STEP 7

Multiply the lowest powers of common prime factors to find the GCF.GCF=21×31=2×3=6 \text{GCF} = 2^1 \times 3^1 = 2 \times 3 = 6 GCF=21×31=2×3=6The greatest common factor of 18 and 24 is 6.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The problem requires finding the greatest common factor (GCF) of the integers 18 and 24.
2. The GCF of two integers is the largest positive integer that divides both of them without leaving a remainder.
3. The Euclidean algorithm is an effective method for finding the GCF of two integers.

1. Identify the prime factorizations of 18 and 24.
2. Compare the prime factorizations to determine the common prime factors.
3. Multiply the common prime factors to find the greatest common factor.

Prime factorize 18.
$18 = 2 \times 3^2$

Prime factorize 24.
$24 = 2^3 \times 3$

Identify the common prime factors between 18 and 24.
The common prime factors are 2 and 3.

Determine the lowest power of each common prime factor.
For the prime number 2, the lowest power is $2^1$ . For the prime number 3, the lowest power is $3^1$ .

Multiply the lowest powers of common prime factors to find the GCF.
$\text{GCF} = 2^1 \times 3^1 = 2 \times 3 = 6$
The greatest common factor of 18 and 24 is 6.