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### Course: Class 10 (Old)>Unit 1

Lesson 3: HCF and LCM

# HCF visualized

Finding the HCF from prime factors can sometimes be hard to imagine. Let's look at an interesting way to visualise finding the HCF of two numbers using prime factorisation. Created by. Created by Aanand Srinivas.

## Want to join the conversation?

• What is main purpose of HCF?
• HCF is useful in cases when you want different amounts of things to be arranged in the same number of order.

For example there are 32 soldiers and 48 bandsman and during the parade you want them to march in the same number of rows. So , you calculate the HCF which is 8 and thus you can make 8 rows each for each group.
• what is the difference HCF and GCF?
• They are the same. HCF is the Highest Common Factor, GCF is the Greatest Common Factor. Greatest means Highest. :) Upvote it please..
• I understand H.C.F BUT, i'm not understanding how you are doing it
• Can you also do this process using the ladder without making this so complicated and soo long?! Because its kinda confusing me? :(
• According to me, if you want to find the HCF, their are many ways. The ladder one is one way of doing it. In that, we must take the two numbers who's HCF we want, beside each other. Then, we find prime numbers that are divisible by both the numbers and then divide the numbers. We carry on this process until we reach 1 by continuously dividing both the numbers. Then we multiply all the prime numbers on the left to get the HCF. If this process is kinda difficult, I'd recommend you to watch and try the Euclid's division algorithm to find HCF - https://youtu.be/H1AE2Se8A5E I found it simple and easy. Hopes that you will too.
(1 vote)
• I don’t understand how to get the hcf at all.Can someone please explain?
(1 vote)
• Sure, I’d be happy to explain how to calculate the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD). The HCF of two or more numbers is the largest number that divides each of them without leaving a remainder.

There are two common methods to find the HCF: the Prime Factorization Method and the Division Method.

1. Prime Factorization Method: This method involves breaking down the numbers into their prime factors.

Step 1: Write each number as a product of its prime factors.
Step 2: List the common factors of both the numbers.
Step 3: The product of all common prime factors is the HCF (use the lower power of each common factor)1.
For example, let’s find the HCF of 60 and 75:

Prime factors of 60 are 2² x 3 x 5 and of 75 are 3 x 5².
The common prime factors are 3 and 5. So, HCF = 3 x 5 = 151.
2. Division Method: This method involves dividing the larger number by the smaller one.

Step 1: Divide the larger number by the smaller number (Larger Number/Smaller Number).
Step 2: Divide the divisor of step 1 by the remainder left (Divisor of step 1/Remainder).
Step 3: Repeat step 2 until there is no remainder. The last divisor is the HCF.
For example, let’s find the HCF of 60 and 48 using this method:

Step 1: Divide 60 by 48. Remainder is 12.
Step 2: Now divide 48 by 12. Remainder is zero, so we stop here.
The last divisor, which is 12, is the HCF.
I hope this helps!
• it is the
Factor tree methord
(1 vote)
• When you say, if a number is divisible by A and also by B, then it will be divisible by A.B too. in fact we shouldn't generalize like that as 12 is divisible by 3 and 6 both, but not by their product. Here the learner will develop misconception. Instead stick to the numbers in the intersection only, and elaborate on that.
(1 vote)
• I guess that there is a another method to do which is division method for finding HCF can we use it ?
(1 vote)
• what do we use hcf in real life for can someone answer pls
• The Highest Common Factor (HCF) has several practical applications in real life. Here are a few examples:

Resource Optimization: HCF can be used to determine the maximum number of equal-sized square tiles that can be used to cover a floor without wasting any tiles1. This concept is also useful in situations where you need to cut ropes of different lengths into smaller pieces of equal length.

Effective Estimation: When planning for an event and you want to ensure that nothing gets wasted, you can use the concept of HCF. For example, if you want to distribute 20 chocolates and 40 sweets among ten children, you would give each child two chocolates and four sweets.

Traffic Signals: The timings of traffic signals are set in such a way that all the lights are not lighting up at one time; especially during peak hours. The controller of these traffic signals calculates the HCF of all the traffic stops to set the timing for each signal.

Parade Organization: HCF is useful when you want different groups to march in the same number of rows. For example, if there are 32 soldiers and 48 bandsmen and during the parade, you want them to march in the same number of rows. So, you calculate the HCF which is 8 and thus you can make 8 rows each for each group.

These are just a few examples. The concept of HCF is widely used in mathematics and other fields to solve problems related to divisibility, fractions, and more. I hope this helps.
(1 vote)
• Are HCF and LCM the same?