Algebra

Finding factors and multiples | Factors and multiples | Pre-Algebra | Khan Academy

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Which of the following numbers is a divisor of 154? A number is a divisor of 154 when we can divide 154 by that number, without a residue. Or another way of understanding – a number is a divisor of 154 if 154 is a multiple of that number. Now let’s look at each of these examples and see which of these is the divisor of 154. 3 does it fit exactly in 154? Or another way, Is 154 a multiple of 3? You will learn later that in fact you can check if something is divisible by 3, by adding the numbers. If the result is divisible by 3, then the whole will be a multiple of 3. We see here that 1 plus 5 is equal to 6. 6 plus 4 is 10. 10 is not divisible by 3. But if you don’t want to use this– we have other videos where we explain this trick in more detail. In fact, you can just divide 154 by 3. 3 is not collected in 1. Enters 5 times in 15. 5 by 3 is 15. Take it out. Then we get 0. Download 4. 3 is collected in 4 once. 1 by 3 is 3. Take it out and you have a remainder of 1. Obviously, 3 is not a divisor of 154. Now how about 5? Each multiple of 5 will have or 5 or 0 at the position of the units. We see that if we write 5 over 1 is 5, 5 over 2 is 10, 5 by 3 is 15, 5 by 4 is 20, we have either 5 or 0 at the position of the units. This number has neither 5 nor 0 at the position of the units, therefore it is not divisible by 5. 5 is not a divisor. 154 is not a multiple of 5. Now let’s see 6. You can use the same method. You can try to divide 6 by 154. If something is divisible by 6, will necessarily be divided into 3, because 6 is divisible by 3. Therefore, we can establish immediately. Since 154 is not divisible by 3, will not be divided into 6. You can try if you want. We can say the same for 9. If something is not divisible by 3, it will not be divisible by 9. because 9 is divisible by 3. This is not divisible by 3, therefore we also exclude 9. We went through it all. 14 seems to be our only option, but let’s actually check. Let’s divide 154 by 14. 14 does not add up to 1. Gathers at 15 exactly once. 1 over 14 is 14. We take it out. We get 1. Take off the four. 14 is collected in 14 once. 1 over 14 is 14. Of course, there is no residue. 14 is added in 154 exactly 11 times. Or 11 over 14 is 154. 154 is a multiple of 14. Let’s solve another one. Which of the following numbers is a multiple of 14? Now we have 14 and we are trying to find its multiples. We can do this in two ways. You can try number by number and try to divide 14 by them, or we can just try to find out which are all multiples of 14. Let’s do it. Let’s try to use the second way. 14 by 1 is 14. You add 14. 14 by 2 is 28. Add another 14. Let’s see, you add 10. You get 38. Then add 4 more times. You get 42. You add another 14. I don’t see any of these numbers coming up yet. Add another 14 to that. We get 56 – not yet. Add another 14. Let’s see, if you add 4, you get 60 and you have to add 10. You get 70. Looks like we found one of those numbers. 70 is a multiple of 14. 14 over 1, 2, 3, 4, 5 – 14 over 5 is 70.

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