The HCF of 40, 35 and 60 is

Options

A. 8
B. 5
C. 10
D. 12

Answer

To find the HCF (Highest Common Factor) of the numbers 40, 35, and 60, we can follow these steps:

### Step-by-Step Solution:

1. **Factorize each number into its prime factors:**
- **For 40:**
- 40 can be divided by 2:
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is a prime number.
- Therefore, the prime factorization of 40 is:
\[ 40 = 2^3 \times 5^1 \]

- **For 35:**
- 35 can be divided by 5:
- 35 ÷ 5 = 7
- 7 is a prime number.
- Therefore, the prime factorization of 35 is:
\[ 35 = 5^1 \times 7^1 \]

- **For 60:**
- 60 can be divided by 2:
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 is a prime number.
- Therefore, the prime factorization of 60 is:
\[ 60 = 2^2 \times 3^1 \times 5^1 \]

2. **Identify the common prime factors:**
- From the factorizations:
- 40 = \(2^3 \times 5^1\)
- 35 = \(5^1 \times 7^1\)
- 60 = \(2^2 \times 3^1 \times 5^1\)
- The only common prime factor among all three numbers is \(5^1\).

3. **Determine the HCF:**
- The HCF is the product of the lowest powers of all common prime factors.
- Here, the only common factor is \(5^1\).
- Therefore, the HCF of 40, 35, and 60 is:
\[ \text{HCF} = 5 \]

### Final Answer:
The HCF of 40, 35, and 60 is **5**.

---