Find the HCF of integers 375 and 675 by the prime factorization method.

To find the Highest Common Factor (HCF) of 375 and 675 using the prime factorization method, follow these steps:

Step 1: Prime factorization of 375

Start by dividing 375 by the smallest prime number, which is 3. 375 ÷ 3 = 125
Next, divide 125 by 5, as it is divisible by 5. 125 ÷ 5 = 25
Finally, divide 25 by 5. 25 ÷ 5 = 5
Then divide 5 by 5 again. 5 ÷ 5 = 1
So, the prime factorization of 375 is: 375 = 3 × 5 × 5 × 5 = 3 × 5³

Step 2: Prime factorization of 675

Start by dividing 675 by 3. 675 ÷ 3 = 225
Divide 225 by 3 again. 225 ÷ 3 = 75
Now, divide 75 by 3. 75 ÷ 3 = 25
Finally, divide 25 by 5. 25 ÷ 5 = 5
Divide 5 by 5. 5 ÷ 5 = 1
So, the prime factorization of 675 is: 675 = 3 × 3 × 3 × 5 × 5 = 3³ × 5²

Step 3: Find the common prime factors The prime factorization of 375 is 3 × 5³, and the prime factorization of 675 is 3³ × 5².

The common prime factors are 3 and 5.

The lowest power of 3 is 3¹.
The lowest power of 5 is 5².
Step 4: Multiply the common factors HCF = 3¹ × 5² = 3 × 25 = 75

Answer: The HCF of 375 and 675 is 75.