How many 4-digit multiples of 7 are there?
All the multiples of 7 would be 7, 14, 21, .... k
where k is the largest 4 digit multiple of 7
This is a AP with a= 7 and d = 7
term(n) = a + (n-1)d
7 + (n-1)(7) < 10000 <---- the smallest 5 digit number
7n < 10000
n < 1428.57.. so there are 1428 multiples of 7 with 4 digits or less
7 + (n-1)7 < 1000 <--- the smallest 4 digit number
7n < 1000
n < 142.8
check: term(142) = 7 + 141*7 = 994
so there are 142 multiples of 7 with 3 digits or less
so 1428 - 142 or 1286 of them are multiples of 7
Sir tell smallest four digits number even multiple of 7
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Well, there are definitely more than zero, that's for sure! But to be more precise, let's try to calculate it together. A 4-digit number starts with the digit 1, 2, 3, 4, 5, 6, 7, 8, or 9, so we have 9 options for the first digit.
Now, let's talk about the second digit. Since we're looking for multiples of 7, it can't be anything, right? Nope! It has to be a number that, when added to the ones digit, results in a multiple of 7. That means we have a bit of flexibility, but a little bit of work too.
The ones digit of a multiple of 7 can be 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, or 98. Well, that's quite a list! But don't worry, to make it simpler, we can cross out the ones that conflict with the options for the first digit (e.g., if the ones digit is 7, the second digit can't be 2 since we already used that as a possibility for the first digit).
By going through this process, you'll see that there are 3 valid options for the second digit.
Now apply the same logic to the third and fourth digits, and you'll find that there are 142 possible 4-digit multiples of 7.
So, in conclusion, the answer is 142, but remember, these numbers are not jokes!
To find the number of 4-digit multiples of 7, we need to determine the range of 4-digit numbers and divide this range by 7.
The smallest 4-digit number is 1000, and the largest 4-digit number is 9999. To find the difference between these two numbers, we subtract the smaller number from the larger number:
9999 - 1000 = 8999.
Now, to find the number of multiples of 7 in this range, we need to divide this difference by 7:
8999 รท 7 = 1285.57.
Since we are looking for whole numbers, we round down to find the number of 4-digit multiples of 7.
Therefore, there are 1285 4-digit multiples of 7.