Question

How many numbers are there between 1000 and 12000 which are divisible by both 21 and 33​

Answer 1

Answer:

47

Step-by-step explanation:

n=12000

count=0

for i in range(1000,n):

if(i%21==0 and i%33==0):

count+=1

print(count)

Answer 2

There are 47 numbers between 1000 and 12000 which are divisible by both 21 and 33

Given :

The numbers between 1000 and 12000 which are divisible by both 21 and 33

To find :

To count the numbers

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 3 :

Find LCM of 21 and 33

We first prime factorise 21 and 33

21 = 3 × 7

33 = 3 × 11

LCM of 21 and 33

= 3 × 7 × 11

= 231

Step 2 of 3 :

Write down the numbers between 1000 and 12000 which are divisible by both 21 and 33

A number which is divisible by both 21 and 33 is also divisible by 231

The numbers between 1000 and 12000 which are divisible by both 21 and 33 are

1155 , 1386, . . . , 11781

Step 3 of 3 :

Count the numbers

The numbers 1155 , 1386, . . . , 11781 forms an arithmetic progression

First term = a = 1155

Common Difference = d = 231

Let number of terms in the AP = n

Then nth term of the AP = 11781

a + ( n - 1 )d = 11781

⇒ 1155 + ( n - 1 ) × 231 = 11781

⇒ 1155 + 231n - 231 = 11781

⇒ 231n + 924 = 11781

⇒ 231n = 10857

⇒ n = 47

Hence there are 47 numbers between 1000 and 12000 which are divisible by both 21 and 33

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