• 3 months ago
Transcript
00:00Hi kids, today we will learn what is HCF and how to calculate HCF, so let's get started.
00:13First of all, HCF stands for Highest Common Factor.
00:19Before learning what is HCF or how we can find HCF, let's learn what are factors.
00:29When we multiply two or more numbers, we get a product, and each number is called a factor
00:36of the product.
00:38Example, 4 multiplied by 5 multiplied by 2 equals 40, then 4, 5 and 2 are factors of
00:5040.
00:51A number is said to be the factor of another, if it can divide the other number completely.
00:58Here, 4, 5, 2 can divide 40 completely, that is, no remainder will be left if we divide
01:0840 with 4, 5 or 2.
01:12So 4, 5 and 2 are factors of 40.
01:19Let's have a look at more examples, 4 multiplied by 5 equals 20, so 4 and 5 are factors of
01:2920.
01:31As 4 and 5 will divide 20 completely, no remainder will be left.
01:39Here we have a number, it's 18.
01:44Now let's see which numbers are factors of 18.
01:49Always remember, 1 is a factor of every number, because 1 can divide any number.
01:5918 divided by 1 is 18, 16 divided by 1 is 16, 17 divided by 1 is 17, 45 divided by 1
02:16is 45, so 1 can divide any number.
02:22So 1 is a factor of every number, and same is for the number itself.
02:29The number itself is always a factor of number, so 1 and 18 are factors of 18.
02:38Also, a number cannot have a factor which is bigger than itself, so factors of 18 can
02:47be between the numbers 1 to 18.
02:52So we have 1 as the smallest factor, and 18 as the largest factor of 18.
03:00Now let's find more factors of 18.
03:05Find numbers that multiply to make 18, 2 multiplied by 9 equals 18.
03:14So 2 and 9 are factors of 18, where 9 will be the second largest factor of 18.
03:25Now 3 multiplied by 6 equals 18, so 3 and 6 are factors of 18.
03:36Now can we multiply 4 with any number to get 18?
03:43You can also see by dividing 18 with 4, if it completely divided 18, then it's a factor.
03:52But no, 4 does not divide 18 completely.
03:58Now can 5 divide 18 completely?
04:02No, so 5 is also not a factor of 18.
04:07Now let's check with 6.
04:10We already have 6 in our factor list.
04:14Now 7, no, 7 cannot divide 18 completely.
04:218, no, 9, yes, 9 can divide 18 completely, and 9 divide 18 into 2, so 9 is also a factor
04:38of 18.
04:40Now one more thing to learn, no other number bigger than 9 can divide 18 completely.
04:49So remember one more thing, factors of a number other than 1 and the number itself cannot
04:57be bigger than the half of a number.
05:01So factors of 18 are 1, 2, 3, 6, 9, and 18.
05:09Now let's learn what is HCF.
05:12HCF, HCF means highest common factor.
05:20Now let's learn finding HCF with an example.
05:24We have two numbers, 6 and 8.
05:29We have to find their HCF, that is the highest common factor.
05:35For finding the highest common factor, we will first find all the factors of 6 and 8.
05:43Let's first find factors of 6.
05:461 multiplied by 6 equals 6, so 1 and 6 are factors of 6.
05:552 multiplied by 3 equals 6, so 2 and 3 are factors of 6.
06:04No other numbers multiply to make 6, so no more factors.
06:101, 2, 3, 6 are the factors of 6.
06:16Now let's find the factors of 8.
06:191 multiplied by 8 equals 8, so 1 and 8 are factors of 8.
06:282 multiplied by 4 equals 8, so 2 and 4 are factors of 8.
06:37No other numbers multiply to make 8, so no more factors.
06:43Hence, 1, 2, 4, and 8 are the factors of 8.
06:51Now find the biggest number out of the common factors of these two numbers.
06:58The numbers 1 and 2 are there in both the lists, that is the factor list of 6 and 8.
07:08So, 1 and 2 are the common factors of 6 and 8.
07:14But we have to find the highest common factor.
07:18Common factors are 1 and 2, and the highest common factor is 2,
07:25as 2 is biggest out of the common factors.
07:30So 2 is the highest common factor of 6 and 8.
07:36So kids, what we did to find the HCF of 6 and 8?
07:43Then we find out the common factors of 6 and 8,
07:47and out of them we found highest common factor.
07:52Now let's take another example.
07:54We have two numbers, 15 and 30.
08:00We have to find their HCF, that is their highest common factor.
08:07So what we have to do?
08:09First of all, find all the factors of 15 and 30.
08:14Let's first find the factors of 15.
08:181 multiplied by 15 equals 15.
08:23So 1 and 15 are factors of 15.
08:283 multiplied by 5 is 15.
08:32So 3 and 5 are factors of 15.
08:36No other numbers multiply to form 15.
08:41So factors of 15 are 1, 3, 5, and 15.
08:48Now let's find factors of 30.
08:521 multiplied by 30 equals 30.
08:56So 1 and 30 are factors of 30.
09:002 multiplied by 15 equals 30.
09:05So 2 and 15 are factors of 30.
09:103 multiplied by 10 equals 30.
09:14So 3 and 10 are factors of 30.
09:205 multiplied by 6 equals 30.
09:24So 5 and 6 are factors of 30.
09:28No other numbers multiply to form 30.
09:33So factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
09:43Now we have listed all the factors of 15 and 30.
09:49Now let's find the common factors of 15 and 30.
09:551, 3, 5, 15 are the common factors of 15 and 30.
10:04And what we have to find?
10:06We have to find the highest common factor.
10:10That is the biggest number out of these common factors.
10:15And the biggest number out of these common factors is 15.
10:20So the highest common factor, or HCF, of 15 and 30 is 15.
10:30Let's take one more example.
10:34We have to find HCF of 23 and 12.
10:39First of all, write factors of 23 and 12.
10:4523 has no factor other than 1 and the number itself.
10:50So it's a prime number.
10:53Prime numbers are those numbers that have only two factors,
10:581 and the number itself.
11:02Now let's find out the factors of 12.
11:051 multiplied by 12 equals 12.
11:09So 1 and 12 are the factors of 12.
11:132 multiplied by 6 equals 12.
11:18So 2 and 6 are factors of 12.
11:223 multiplied by 4 equals 12.
11:27So 3 and 4 are factors of 12.
11:32No other numbers multiply to make 12.
11:36So no more factors.
11:391, 2, 3, 4, 6, and 12 are factors of 12.
11:47Now let's find the common factors.
11:50The only common factor here is 1.
11:54So HCF is also 1.
11:58Kids, remember one thing.
12:01HCF of two prime numbers is always 1.
12:06For example, HCF of 7 and 13 will be 1.
12:13HCF of 23 and 17 will be 1.
12:19HCF of 3 and 5 will be 1.
12:24So kids, today we learned what is HCF and how to find HCF.
12:31Now you may go ahead and take a quiz to learn more.
12:35Bye-bye.