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If A and B are multiples of C, then A + B is also a multiple of C:

If A is a multiple of C then A = mC for some integer m

If B is a multiple of C, then B = nC for some integer n

→ A + B = mC + nC

= (m + n)C

= kC where k = m + n and is an integer

→ A + B is a multiple of C

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6y ago
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6y ago

(A + B) is a multiple of C, as is (A - B).

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Q: When A B and C are counting numbers and both A and B are multiples of C what can you say about A plus B?
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How many two-digit counting numbers are either multiples of 2 or multiples of 3?

45 multiples of 2 plus 30 multiples of 3 minus 15 multiples of 6 equals 60 numbers


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225 and if you mean both(all the numbers) it is 450


How many numbers from 1 to 100 are multiples of 2 3 4 6 8 9?

Assuming you mean that you want the number of multiples of each, then for 1-100: number of multiples of 2 = 50 number of multiples of 3 = 33 number of multiples of 4 = 25 number of multiples of 6 = 16 number of multiples of 8 = 12 number of multiples of 9 = 11 Assuming you mean that you want the numbers that are multiples of 2, 3, 4, 6, 8 or 9, then some numbers may be multiples of more than one (for example 12 is a multiple of 2, 3, 4 and 6) and so a straight addition of the number of multiples of each cannot be done: Consider 2, 4 and 8 Every multiple of 4 or 8 is also a multiple of 2, so all the multiples of 4 and 8 are counted by the multiples of 2. Consider 3 and 9 Every multiple of 9 is also a multiple of 3, so all the multiples of 9 are counted by the multiple of 3 Consider 2, 3 and 6. Every multiple of 6 is an even multiple of 3, so are counted in both the multiples of 2 and 3. So the total number of multiples of 2, 3, 4, 6, 8 or 9 is the number of multiples of 2 plus the number of multiples of 3 minus the number of multiples of 6: For 1 to 100, Number of multiples of 2 = 50 Number of multiples of 3 = 33 Number of multiples of 6 = 16 So number of multiples of 2, 3, 4, 6, 8 or 9 in 1-100 is 50+33-16 = 67. Assuming you mean that they are multiples of all of 2, 3, 4, 6, 8 and 9, then they must be multiples of the lowest common multiple of 2, 3, 4, 6 ,8, 9 2 = 21, 3 = 31, 4 = 22, 6 = 2131, 8 = 23, 9 = 32 LCM = highest power of the primes used = 2332 = 72 Thus all numbers that are multiples of 2, 3, 4, 6, 8 and 9 are multiples of 72, which means between 1 and 100 only 1 number is a multiple of all of them, namely 72

Related questions

How many two-digit counting numbers are either multiples of 2 or multiples of 3?

45 multiples of 2 plus 30 multiples of 3 minus 15 multiples of 6 equals 60 numbers


What percentage of numbers are multiples of 3 or 8 using numbers from 1-100?

33 multiples of 3 plus 12 multiples of 8 minus 4 multiples of both. 41%


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(Every counting number) plus (a zero tacked on to the end of it) is one of them.


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The whole numbers include the counting numbers, plus zero.


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What natural numbers are whole numbers?

The set of counting numbers is the positive integers. The set of whole numbers is the positive integers plus zero. The term "natural numbers" has been used interchangeably with both of those sets.


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Whole numbers are known as zero plus the "counting numbers." (1, 2, 3, ...) So, the whole numbers of 21 would be 0 - 21. (23 numbers.)


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there aren't any as otherwise they wouldn't be prime numbers


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Any domain that you like. It can be the counting numbers, integers, rationals, reals or complex numbers. Or it can be a subset of any of them. For example, the domain could be {-2, 7, 3.56}.