Because 2 is a factor of 4. If a number is a multiple of four, when you add that it is a multiple of 2 there is no extra information, no additional factor.
No, but vice versa holds true. Case and point: 6 is a multiple of 2, but not a multiple of 4. 8 is a multiple of 4, and is a multiple of 2. Because a factor of 4 is 2, every multiple of 4 is also a multiple of 2. But since 4 is not a factor of 2, rather, only half of it, only half of the multiples of 2 will be multiples of 4.
Since 8 is a multiple of 2 and 4, all multiples of 8 are also multiples of both of them. Thus, Jose and maria are both correct.
No. All it needs is one counter example to disprove: 6 is a multiple of 2 but NOT a multiple of 4.
2 and 4 are factors of 8. 8 is a multiple of 2 and 4.
The Least Common Multiple (LCM) for 2 4 is 4.
Because 6 is a multiple of 2 and not of 4.
If ordered by size, only every other multiple of 2 is a multiple of 4. All multiples of 4 are multiples of 2.
No, but vice versa holds true. Case and point: 6 is a multiple of 2, but not a multiple of 4. 8 is a multiple of 4, and is a multiple of 2. Because a factor of 4 is 2, every multiple of 4 is also a multiple of 2. But since 4 is not a factor of 2, rather, only half of it, only half of the multiples of 2 will be multiples of 4.
It's not. 4 is a multiple of 2. 2 is a factor of 4 because it can divide into 4 evenly with no remainder.
because... 4 does not go into 2 so it's not a multiple All multiples of 4 are multiples of 2.
All multiples of 4 are multiples of 2 and 4.
Because 20 is a multiple of 4. All multiples of 20 are also multipples of 2, 5 and 10
Since 8 is a multiple of 2 and 4, all multiples of 8 are also multiples of both of them. Thus, Jose and maria are both correct.
No. All it needs is one counter example to disprove: 6 is a multiple of 2 but NOT a multiple of 4.
Since 4 is a multiple of 2, all the multiples of 4 will be common.
A common multiple of two integers 'x' and 'y', are the multiples of 'x' which are also multiples of 'y'.For your example, because 12 is itself a multiple of 4, ALL multiples of 12 are common multiples of 4 and 12.To prove my point, I will list out the multiples of both 4 and 12:multiples of 4:4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96, 100...multiples of 12:12,24,36,48,60,72,84,96...You can see here that every multiple of 12, is also a multiple of 4, thus all multiples of 12 are common multiples for 4 and 12.Also..a quick easy list:12,24,36,48,60,72,84,96and if you didn't read above, because 12 is a multiple of for, all multiples of 12 are a multiple of 4 .. simple!
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