Lareina understands factors, but sometimes she has trouble finding all the factors of a number. What advice would you give to help her find all the factors of a number? Demonstrate by finding all the factors of 110.
start with the smallest possible factor. Divide by it as many times as possible, then move on to the next prime factor, and repeat until you have reached a prime number.
110 = 2 * 55
3 does not divide 55
55 = 5 * 11
There are no other prime factors, so
110 2*5*11
720 = 2*2*2*2*45
45 = 3*3*5
so, 720 = 2^4 3^2 5
Math is cool
To find all the factors of a number, here's a step-by-step process you can follow:
1. Start by listing the numbers that can evenly divide the given number, which we'll call the dividend.
2. Begin with the smallest possible factor, which is 1. Write it down on a piece of paper.
3. Move on to the next number, 2, and check if it divides the dividend evenly without leaving a remainder. If it does, write it down. Otherwise, move to the next number.
4. Continue this process, checking if each subsequent number divides the dividend evenly. If it does, write it down; otherwise, proceed to the next number.
5. Keep repeating this process until you reach the square root of the dividend. After that point, you'll find the same factors in reverse order.
6. Finally, include the dividend itself as a factor.
Now let's apply this method and find all the factors of 110:
1. Start with 1 (since every number is divisible by 1), and write it down: 1.
2. Check if 2 divides 110 without a remainder. It does, so we write it down: 1, 2.
3. Move to the next number, 3, and see if it divides 110. It doesn't.
4. Continue to the next number, 4, which does not divide 110 evenly.
5. Check if 5 divides 110 evenly. It does, so we add it to the list: 1, 2, 5.
6. Proceed to 6, which doesn't divide 110 evenly.
7. Check 7, which is not a factor of 110.
8. Now, let's try 8. We discover that it doesn't divide 110 evenly.
9. Proceed to 9, which is also not a factor of 110.
10. Check if 10 divides 110 evenly. It does, so we add it to the list: 1, 2, 5, 10.
11. Continue the process until we reach the square root of 110, which is approximately 10.49.
12. Include the dividend itself, 110, as a factor.
Thus, the factors of 110 are: 1, 2, 5, 10, 11, 22, 55, and 110.