Question

How many numbers between 540 and 950 are divislible by both 3 and 7?​

Answer 1

Answer:

25t57

Step-by-step explanation:

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Answer 2

Answer:

The numbers between 540 and 950 that are divisible by both 3 and 7 =  21

Step-by-step explanation:

To find,

The numbers between 540 and 950 that are divisible by both 3 and 7

Solution:

Recall the formula,

The number of terms of AP = n = $\frac{a_n - a}{d} +1$, -------------(1)

Where a is the first term, aₙ is the nth term and d is the common difference of the AP.

The number between 540 and 950, that are divisible by 3 are

{543, 546,549,552,...............................948}

The number between 540 and 950, that are divisible by 7 are

{546, 553, 560,........945}

The numbers that are divisible by both 3 and 7 are the numbers that are multiples of LCM(3,7) = 21

{546,567, 588,............945}

Let A be the set of all numbers between  540 and 950 divisible by 21.

Thes,A =  {546,567, 588,............945}

The set of elements of set A , form an AP with first term  = 546 and common difference = 21

Required to find, the number of terms of this AP.

Substituting equation (1), the number of terms of the AP  

n = $\frac{945 - 546}{21}+1$

= $\frac{399}{21}+1$

= 19 +1

= 20

The number of elements of the set A = 21

∴The numbers between 540 and 950 that are divisible by both 3 and 7 =  21

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