Short Question

Factorisation:HCF and LCM : Short Question

1 What is factorization?

Factorization is the process of breaking down a number into smaller numbers that, when multiplied together, give the original number. These smaller numbers are called factors. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because: 12=2×6 12=3×4

2 What is the HCF (Highest Common Factor)?

The HCF of two or more numbers is the largest number that is a factor of all the given numbers. For example, to find the HCF of 12 and 18: • Factors of 12: 1, 2, 3, 4, 6, 12 • Factors of 18: 1, 2, 3, 6, 9, 18 • Common factors: 1, 2, 3, 6 • HCF: 6 (the largest common factor)

3 What is the LCM (Least Common Multiple)?

The LCM of two or more numbers is the smallest number that is a multiple of all the given numbers. For example, to find the LCM of 4 and 5: Multiples of 4: 4, 8, 12, 16, 20, 24, ... Multiples of 5: 5, 10, 15, 20, 25, 30, ... LCM: 20 (the smallest common multiple)

4 How do you find the HCF of two numbers?

To find the HCF, you can use the following steps: List all the factors of each number. Identify the common factors. The largest common factor is the HCF.

5 Why are HCF and LCM important?

HCF and LCM are important in solving problems involving fractions, ratios, and in real-life situations where you need to combine things into groups or break things into parts evenly.

6 Can you give an example where HCF is used?

Imagine you have two pieces of ribbon, one 12 meters long and the other 18 meters long, and you want to cut them into the longest equal lengths possible without wasting any ribbon. You would find the HCF of 12 and 18, which is 6 meters. So, you can cut both ribbons into 6-meter pieces.

7 Can you give an example where LCM is used?

If two traffic lights change every 3 minutes and 4 minutes respectively, and you want to know when they will change at the same time, you would find the LCM of 3 and 4, which is 12 minutes. So, they will both change at the same time every 12 minutes.

8 What are prime factors?

Prime factors are factors of a number that are prime numbers. For example, the prime factors of 30 are 2, 3, and 5 because: 30=2×3×5

9 How do you use prime factorization to find HCF and LCM?

For HCF: Find the prime factors of each number, then multiply the smallest power of all common prime factors. For LCM: Find the prime factors of each number, then multiply the highest power of all prime factors.

10 Relationship between HCF and LCM mathematically?

HCF×LCM=Product of the two numbers

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