Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To find the highest common factor (HCF) of 90 and 252, you can follow these steps:
1. Prime Factorization:
First, we need to prime factorize both numbers.
- Prime factorization of 90:
[tex]\[ 90 = 2 \times 3^2 \times 5 \][/tex]
- Prime factorization of 252:
[tex]\[ 252 = 2^2 \times 3^2 \times 7 \][/tex]
2. Identify Common Factors:
Next, identify the common prime factors between 90 and 252.
- Common prime factors: [tex]\( 2 \)[/tex] and [tex]\( 3^2 \)[/tex]
3. Select Least Power of Common Factors:
From the common prime factors, select the least power of each:
- For [tex]\( 2 \)[/tex]: The least power is [tex]\( 2^1 \)[/tex]
- For [tex]\( 3 \)[/tex]: The least power is [tex]\( 3^2 \)[/tex]
4. Multiply the Common Factors:
Multiply these selected powers to find the HCF:
[tex]\[ \text{HCF} = 2^1 \times 3^2 \][/tex]
Calculate the product:
[tex]\[ 2^1 = 2 \][/tex]
[tex]\[ 3^2 = 9 \][/tex]
[tex]\[ \text{HCF} = 2 \times 9 = 18 \][/tex]
Therefore, the highest common factor (HCF) of 90 and 252 is [tex]\( \boxed{18} \)[/tex].
1. Prime Factorization:
First, we need to prime factorize both numbers.
- Prime factorization of 90:
[tex]\[ 90 = 2 \times 3^2 \times 5 \][/tex]
- Prime factorization of 252:
[tex]\[ 252 = 2^2 \times 3^2 \times 7 \][/tex]
2. Identify Common Factors:
Next, identify the common prime factors between 90 and 252.
- Common prime factors: [tex]\( 2 \)[/tex] and [tex]\( 3^2 \)[/tex]
3. Select Least Power of Common Factors:
From the common prime factors, select the least power of each:
- For [tex]\( 2 \)[/tex]: The least power is [tex]\( 2^1 \)[/tex]
- For [tex]\( 3 \)[/tex]: The least power is [tex]\( 3^2 \)[/tex]
4. Multiply the Common Factors:
Multiply these selected powers to find the HCF:
[tex]\[ \text{HCF} = 2^1 \times 3^2 \][/tex]
Calculate the product:
[tex]\[ 2^1 = 2 \][/tex]
[tex]\[ 3^2 = 9 \][/tex]
[tex]\[ \text{HCF} = 2 \times 9 = 18 \][/tex]
Therefore, the highest common factor (HCF) of 90 and 252 is [tex]\( \boxed{18} \)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.