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].
