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Factoring is crucial to algebra and any math built on algebra. Like any other skill you get better at this one with practice, but it helps to have a method. I like to do both ends against the middle. By that I mean, if you think of 72 as a number line, what you want to do is find the factors at the ends and work you way to the middle of the line, that way you only have to test the smaller half of the number line. Having an orderly system means that you will be sure not to miss any and get there faster. You can always just try them all but for larger numbers that would be time consuming. Here goes...
All numbers are divisible by 1 and by themselves.
1 x 72 = 72
So, we now have 1, 72
72 is an even number so it is also divisible by 2.
2 x 36 = 72
So, now we have 1, 2, 36, 72
Any other numbers we find will be between 2 and 36, less that half of the total numbers!
I know that 72 is divisible by 3. If you add the digits of a number together and get a multiple of 3, the original number is also a multiple of 3! 7 + 2 = 9. Yep. (Special bonus, if they add up to 9, the original number is also divisible by 9.)
3 x 24 = 72
Now we have 1,2,3,24,36,72
Now, this number is also divisible by 4. You can see that some of the factors are divisible by 4.
4 x 18 = 72
Now it's 1,2,3,4,18,24,36,72
We can rule out 5. It doesn't end in 0 or 5.
It is definitely divisible by 6. 2 and 3 are factors and they make 6.
6 x 12 = 72
We are getting very close to the middle now. 6 and 12 are pretty close.
1,2,3,4,6,12,18,24,36,72
7 won't work. 7 goes into 70 (obviously) and cannot go into 72.
8 is easy. We have 2 and 4 so we have to have 8.
8 x 9 = 72
Hey, those meet! That means we are done. There aren't any other numbers left to test.
The final answer is 1,2,3,4,6,8,9,12,18,24,36,72.
Frequently, you just need the "prime factors." That means that if you list 2 or 3 you don't need to list 4 or 9 as well, or if you list 2 and 3 you don't need to list 12. Prim numbers only have two factors, 1 and itself.
So, 2 is prime (it is the only even prime). It factors to 1 and 2.
But, 4 is not prime. It factors to 1, 2, 4.
The prime factors of 72 are 1,2,3. That's it. All the other factors are just multiples of 2 and 3.
Later in math you will learn a faster way to do this using the quadratic formula so don't worry about having to do this forever.
Hope this helps!
D
What else can I help you with?
What two numbers multiply to get 72?
Two numbers that you can multiply together to get 72 are: 36 and 2.
What are all the numbers that 72 is divisible by?
1,2,3,4,6,8,9,12,18,24,36,72
What two numbers times to 72?
Well, isn't that a happy little question! If we're looking for two numbers that multiply to 72, we can think of them as partners dancing together. One pair that comes to mind is 8 and 9 - when they twirl and spin together, they create the beautiful number 72. Remember, there are many different pairs of numbers that can work together in harmony to create 72, so feel free to explore and find the one that speaks to you!
What is the mean data for the numbers 72 73 74 75 and 76?
Mean simply means average. To find the average of a set of numbers, simply add them all together and then divide by the amount of numbers you added. 72 + 73 + 74 + 75 + 76 = 370 370 ÷ 5 = 74. The mean of {72, 73, 74, 75, 76} is 74, which is also the median.
What is 72x5?
To find the product of 72 and 5, you simply multiply the two numbers together. 72 multiplied by 5 equals 360. This can be calculated by adding 72 five times, or by using the distributive property to break down the multiplication into smaller, more manageable steps.
What two numbers add together to make -20 but times together to give 72?
-15.2915 and -4.7085 (approx).
Can 72 be divided by anything?
yes, 36 can go into 72 2times, 24 can go into 72 3 times, 18 can go into 72 4 times, these are all the whole numbers that can go into 72.
What two negative numbers when multiplied together equal 72?
Negative 2 and negative 36 multiplied together equal 72 -2 x -36 = 72 Remember when you multiply two negative numbers together you get a postivie number. Since 72 is an even number it has to be divisible by 2 so if you divide it by 2 the number you get (36) times 2 equals 72.
What two numbers multiply to get 72?
Two numbers that you can multiply together to get 72 are: 36 and 2.
What two numbers multiply together to equal -1008 and add together to equal 72?
-936
6 times what equals 72?
72 / 6 = 12 Therefore 12 * 6 = 72
What numbers can you multiply together to get -432 that also add together to get -66?
-498
What is a factor pairs of 72?
The factor pairs of 72 are pairs of numbers that can be multiplied together to give the number 72. The factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). These pairs represent all the combinations of numbers that, when multiplied, result in 72.
What are all the numbers that 72 is divisible by?
1,2,3,4,6,8,9,12,18,24,36,72
What prime numbers multiplied together make 1225?
1225 = 52*72
What two numbers times to 72?
Well, isn't that a happy little question! If we're looking for two numbers that multiply to 72, we can think of them as partners dancing together. One pair that comes to mind is 8 and 9 - when they twirl and spin together, they create the beautiful number 72. Remember, there are many different pairs of numbers that can work together in harmony to create 72, so feel free to explore and find the one that speaks to you!
One number is 5 times a second number The sum of the numbers is 72. What are the numbers?
12 and 60 ============ a + b = 72 a = 5b replacing a by 5b in the first equation 5b + b = 72 6b = 72 b = 12 72 - 12 = 60
