Question

How many three-digit multiples of 6 have the sum of digits divisible by 6 if all digits are different?

Answer 1

Answer:

Substitute a = 102, l = 996 and d = 6. So, number of 3 digit numbers divisible by 6 is 150. Substitute a = 102, d = 6, l = 996 and n = 150. So, the sum of all 3 digit numbers divisible by 6 is 82350.

Step-by-step explanation:

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Answer 2

Answer:-

• Sum of all 3 digit natural multiples of 6 is 82,350.

Solution:-

Three digits natural multiples of 6 would be 102 , 108, 114, 120 ... 996

From the given numbers we can write that it is an AP.

• → a = 102
• → d = 6

to calculate the sum of all terms we had to calculate the total number of element in the AP, from its last term

let the last term be nth term

• → 996 = 102 +(n-1) 6
• → 996-102 = (n-1) 6
• → (n-1)6 = 894
• → n-1 = 894/6
• → n-1 = 149
• → n= 149+1
• → n = 150

Sum of all 3 digit natural multiples of 6 are

• → = n/2( a+l)
• → = 150/2( 102+996)
• → = 150/2(1098)
• → = 150(549)
• → = 82,350

sum of all 3 digit natural multiples of 6 is 82,350.

Hope it helps you.!!