Math / Numbers & Operations

QuestionFind the highest common factor of the numbers 45, 120, and 180.

Studdy Solution

STEP 1

1. We need to find the highest common factor (HCF) of the numbers 45, 120, and 180.
2. The HCF is the largest number that divides each of the given numbers without leaving a remainder.

STEP 2

1. Find the prime factors of each number.
2. Identify the common prime factors.
3. Calculate the HCF by multiplying the common prime factors.

STEP 3

Find the prime factors of 45.
- Divide 45 by 3: $45 \div 3 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 45 are $3^2 \times 5$ .

STEP 4

Find the prime factors of 120.
- Divide 120 by 2: $120 \div 2 = 60$ - Divide 60 by 2: $60 \div 2 = 30$ - Divide 30 by 2: $30 \div 2 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 120 are $2^3 \times 3 \times 5$ .

STEP 5

Find the prime factors of 180.
- Divide 180 by 2: $180 \div 2 = 90$ - Divide 90 by 2: $90 \div 2 = 45$ - Divide 45 by 3: $45 \div 3 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 180 are $2^2 \times 3^2 \times 5$ .

STEP 6

Identify the common prime factors among 45, 120, and 180.
- Common prime factors are $3$ and $5$ .

STEP 7

Calculate the HCF by multiplying the lowest power of all common prime factors.
- The lowest power of $3$ is $3^1$ . - The lowest power of $5$ is $5^1$ .
Thus, the HCF is $3^1 \times 5^1 = 15$ .
The highest common factor of 45, 120, and 180 is:
$\boxed{15}$

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QuestionFind the highest common factor of the numbers 45, 120, and 180.

Studdy Solution

STEP 1

1. We need to find the highest common factor (HCF) of the numbers 45, 120, and 180.
2. The HCF is the largest number that divides each of the given numbers without leaving a remainder.

STEP 2

1. Find the prime factors of each number.
2. Identify the common prime factors.
3. Calculate the HCF by multiplying the common prime factors.

STEP 3

Find the prime factors of 45.
- Divide 45 by 3: $45 \div 3 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 45 are $3^2 \times 5$ .

STEP 4

Find the prime factors of 120.
- Divide 120 by 2: $120 \div 2 = 60$ - Divide 60 by 2: $60 \div 2 = 30$ - Divide 30 by 2: $30 \div 2 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 120 are $2^3 \times 3 \times 5$ .

STEP 5

Find the prime factors of 180.
- Divide 180 by 2: $180 \div 2 = 90$ - Divide 90 by 2: $90 \div 2 = 45$ - Divide 45 by 3: $45 \div 3 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 180 are $2^2 \times 3^2 \times 5$ .

STEP 6

Identify the common prime factors among 45, 120, and 180.
- Common prime factors are $3$ and $5$ .

STEP 7

Calculate the HCF by multiplying the lowest power of all common prime factors.
- The lowest power of $3$ is $3^1$ . - The lowest power of $5$ is $5^1$ .
Thus, the HCF is $3^1 \times 5^1 = 15$ .
The highest common factor of 45, 120, and 180 is:
$\boxed{15}$

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QuestionFind the highest common factor of the numbers 45, 120, and 180.

Studdy Solution

STEP 1

1. We need to find the highest common factor (HCF) of the numbers 45, 120, and 180.2. The HCF is the largest number that divides each of the given numbers without leaving a remainder.

STEP 2

1. Find the prime factors of each number.2. Identify the common prime factors.3. Calculate the HCF by multiplying the common prime factors.

STEP 3

Find the prime factors of 45.- Divide 45 by 3: 45÷3=15 45 \div 3 = 15 45÷3=15 - Divide 15 by 3: 15÷3=5 15 \div 3 = 5 15÷3=5 - 5 is a prime number.Thus, the prime factors of 45 are 32×5 3^2 \times 5 32×5.

STEP 4

STEP 5

STEP 6

Identify the common prime factors among 45, 120, and 180.- Common prime factors are 3 3 3 and 5 5 5.

STEP 7

Calculate the HCF by multiplying the lowest power of all common prime factors.- The lowest power of 3 3 3 is 31 3^1 31. - The lowest power of 5 5 5 is 51 5^1 51.Thus, the HCF is 31×51=15 3^1 \times 5^1 = 15 31×51=15. The highest common factor of 45, 120, and 180 is:15\boxed{15}15​

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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. We need to find the highest common factor (HCF) of the numbers 45, 120, and 180.
2. The HCF is the largest number that divides each of the given numbers without leaving a remainder.

1. Find the prime factors of each number.
2. Identify the common prime factors.
3. Calculate the HCF by multiplying the common prime factors.

Find the prime factors of 45.
- Divide 45 by 3: $45 \div 3 = 15$ - Divide 15 by 3: $15 \div 3 = 5$ - 5 is a prime number.
Thus, the prime factors of 45 are $3^2 \times 5$ .

Identify the common prime factors among 45, 120, and 180.
- Common prime factors are $3$ and $5$ .

Calculate the HCF by multiplying the lowest power of all common prime factors.
- The lowest power of $3$ is $3^1$ . - The lowest power of $5$ is $5^1$ .
Thus, the HCF is $3^1 \times 5^1 = 15$ .
The highest common factor of 45, 120, and 180 is:
$\boxed{15}$