### Find LCM of 16 and 24

The LCM of two numbers is and their HCF is If one of the The maximum number of boys or girls in each group will be (a) 11 (b) 17 (c) 24 (d) 36 The least among the fractions 16 15, 19 20, 24 35, 34 35 is How many The H.C.F. and L.C.M. of two numbers are 12 and respectively. electricity bill is paid before due date, one gets a reduction of 4% on the amount of the bill. The sets of multiples are {8, 16, 24, 32, 40, 48, 56, 64, 72, } Find the greatest common factor and least common multiple by the prime factorization method. 1.

**GCD (16, 24, 36)**

We say that number of factors of a given number are finite. What are the multiples of 7? Check this for the multiples of 6, 9 and Write the multiples of 5. The list is endless. We find that the number of multiples of a given number is infinite. Can 7 be a multiple of itself? Try it with 3, 12 and You will find that every number is a multiple of itself. The factors of 6 are 1, 2, 3 and 6.

The sum of the factors of 28 is equal to twice the number The numbers 6 and 28 are perfect numbers. Is 10 a perfect number? Find all the multiples of 9 upto We find that a The number 1 has only one factor i. These numbers are prime numbers. Try to find some more prime numbers other than these. These numbers are composite numbers. This method was given by a Greek Mathematician Eratosthenes, in the third century B.

List all numbers from 1 toas shown below. Cross out 1 because it is not a prime number. Encircle 2, cross out all the multiples of 2, other than 2 itself, i. You will find that the next uncrossed number is 3. The next uncrossed number is 5. Write all the prime numbers less than These are called even numbers.

You can verify that a two digit number or a three digit number is even or not. How will you know whether a number like is even? By dividing it by 2.

## NCERT Class VI Mathematics Chapter 3 Playing with Numbers

Will it not be tedious? We say that a number with 0, 2, 4, 6, 8 at the ones place is an even number. So, are even numbers. Let us try to find some interesting facts: It is again 2. Thus, 2 is the smallest prime number which is even.

Of course not, they are all odd. Thus, we can say that every prime number except 2 is odd. What is the sum of any two a Odd numbers? State whether the following statements are True or False: The numbers 13 and 31 are prime numbers. Find such pairs of prime numbers upto Write down separately the prime and composite numbers less than What is the greatest prime number between 1 and 10? Express the following as the sum of two odd primes.

Give three pairs of prime numbers whose difference is 2. Two prime numbers whose difference is 2 are called twin primes]. Which of the following numbers are prime?

Express each of the following numbers as the sum of three odd primes: Write five pairs of prime numbers less than 20 whose sum is divisible by 5. Fill in the blanks: Let us see whether we can find a pattern that can tell us whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or She finds that if a number has 0 in the ones place then it is divisible by Can you find out the divisibility rule for ?

Look at the units place. Again these numbers have either 0 or 5 in their ones places. He tried to divide the numbers 23, 56, 97 by 5. Will he be able to do that? Is divisible 5? She finds some pattern in the ones place of these numbers. Can you tell that? She divides these numbers by 2 and gets remainder 0.

She also finds that the numbersare not divisible by 2. Are the numbers 21, 27, 36, 54, divisible by 3? Are the numbers 25, 37, divisible by 3?

Can you see any pattern in the ones place? Do you observe anything special? All these additions are divisible by 3. Add the digits in 25, 37, These are not divisible by 3. Is divisible by 3? One such number is Think of such 4-digit numbers.

Observe the number formed by the ones and tens places of For it is 36, again divisible by 4. Is the number divisible by 4?

Is 86 divisible by 4? Check this rule by taking ten more examples. Divisibility for 1 or 2 digit numbers by 4 has to be checked by actual division. Are the numbers, divisible by 8? You can check that they are divisible by 8. Let us try to see the pattern. Look at the digits at ones, tens and hundreds place of these numbers.

These too are divisible by 8. You will find that the numbers themselves are divisible by 8. Is divisible by 8? Do you find any pattern when the digits of these numbers are added? Is the number divisible by 9? The numbersand are all divisible by We form a table and see if the digits in these numbers lead us to some pattern.

We observe that in each case the difference is either 0 or divisible by The number is also not divisible by These two numbers have only 1 as the common factor. What about 7 and 16? Thus, 4 and 15 are co-prime numbers.

- Steps for Finding the LCM
- Steps for Finding the LCM
- Least Common Multiple of 16 and 24 with GCF Formula

Are 7 and 15, 12 and 49, 18 and 23 co-prime numbers? Factors of 4 are 1, 2 and 4. Factors of 12 are 1, 2, 3, 4, 6 and Factors of 16 are 1, 2, 4, 8 and Clearly, 1, 2 and 4 are the common factors of 4, 12, and Find the common factors of a 8, 12, 20 b 9, 15, Let us now look at the multiples of more than one number taken at a time.

The multiples of 4 are 4, 8, 12, 16, 20, 24, … write a few more The multiples of 6 are 6, 12, 18, 24, 30, 36, … write a few more Out of these, are there any numbers which occur in both the lists? We observe that 12, 24, 36, … are multiples of both 4 and 6. Can you write a few more? They are called the common multiples of 4 and 6. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, … Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, … Multiples of 6 are 6, 12, 18, 24, 30, … Common multiples of 3, 5 and 6 are 30, 60, … Write a few more common multiples of 3, 5 and 6.

Find the common factors of 75, 60 and Factors of 75 are 1, 3, 5, 15, 25 and Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 30 and Factors of are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, and Thus, common factors of 75, 60 and are 1, 3, 5 and Find the common multiples of 3, 4 and 9. Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48,… Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, … Clearly, common multiples of 3, 4 and 9 are 36, 72, ,… EXERCISE 3.

A number is divisible by both 5 and A number is divisible by Write the quotient and the number which is not divisible by the above prime number in the second row.

In the second row, write the quotient we get after the division of 24 by 2. Since 15 is not divisible by 2 write 15 in the second row as it is. Divide the numbers with another least prime number. Continue division until the remainder is a prime number or 1. Multiply all the divisors and remaining prime number if any to obtain the LCM.

Given natural numbers are written as the product of prime factors. To obtain the highest common factor multiply all the common prime factors with the lowest degree power. Find the HCF of 20 and 12 by prime factorization method. To find HCF of 20 and 12 write each number as a product of prime factors. Multiply all the common prime factors with the lowest degree.

Here we have only 2 as a common prime factor with the lowest power of 2. In this method divide the largest number by the smallest number of the given numbers until the remainder is zero. The last divisor will be the HCF of given numbers. Divide the largest number by the smallest number. Here, the largest number is 24 and the smaller one is Divide 24 by 15 Step 2: Take divisor as new dividend and remainder as the new divisor, i.

### What is the greatest common factor of 24 and 48? | colorky.info

Proceed this still the remainder is zero and the last divisor will be the HCF of the given numbers. Therefore, HCF of 24 and 15 is 3. Alternatively, we can divide both the numbers by the least common prime factor still there is no more common prime factor.

Multiply all divisors to get the HCF of given numbers. Consider the above example, HCF of 24 and 15 can be calculated by following steps: