Find H.C.F and L.C.M of the following numbers 8, 9 and 25.

To find the Highest Common Factor (H.C.F) and the Lowest Common Multiple (L.C.M) of the numbers 8, 9, and 25, we can use a systematic approach. Let's break it down step by step.

Finding the H.C.F

The H.C.F, also known as the greatest common divisor, is the largest number that divides all the given numbers without leaving a remainder. To find the H.C.F, we can use the prime factorization method.

Step 1: Prime Factorization

• 8: The prime factorization of 8 is 2 × 2 × 2, or 2³.
• 9: The prime factorization of 9 is 3 × 3, or 3².
• 25: The prime factorization of 25 is 5 × 5, or 5².

Step 2: Identify Common Factors

Next, we look for common prime factors among the numbers. In this case, the prime factors are:

• 8: 2³
• 9: 3²
• 25: 5²

Since there are no common prime factors among 8, 9, and 25, the H.C.F is 1.

Calculating the L.C.M

The L.C.M is the smallest number that is a multiple of all the given numbers. To find the L.C.M, we can also use the prime factorization method.

Step 1: Use Prime Factorization

From our earlier factorization, we have:

• 8 = 2³
• 9 = 3²
• 25 = 5²

Step 2: Take the Highest Power of Each Prime Factor

To find the L.C.M, we take the highest power of each prime factor present in the factorizations:

• For 2, the highest power is 2³.
• For 3, the highest power is 3².
• For 5, the highest power is 5².

Step 3: Multiply the Highest Powers Together

Now, we multiply these together to find the L.C.M:

L.C.M = 2³ × 3² × 5²

Calculating this gives:

• 2³ = 8
• 3² = 9
• 5² = 25

Now, multiply them:

8 × 9 = 72

72 × 25 = 1800

Final Results

Thus, the H.C.F of 8, 9, and 25 is 1, and the L.C.M is 1800.