what is the prime factorization of 120
To find the prime factorization of 120, follow these steps:
Step 1: Start by finding the smallest prime number that divides 120 evenly. In this case, 2 is the smallest prime number that divides 120 without a remainder. Therefore, divide 120 by 2 to get:
120 ÷ 2 = 60
Step 2: Now, repeat the process with the quotient from the previous step, which is 60. Divide 60 by the smallest prime number, which is 2, again:
60 ÷ 2 = 30
Step 3: Continue dividing the quotient from step 2 by the smallest prime number. Divide 30 by 2:
30 ÷ 2 = 15
Step 4: To keep simplifying the quotient, divide 15 by the smallest prime factor, which is 3:
15 ÷ 3 = 5
Step 5: At this point, we have reached a prime number, which is 5. Since 5 cannot be divided any further, we stop the process.
Step 6: Finally, write down all the prime factors we used to divide 120:
2 × 2 × 2 × 3 × 5 = 120
Therefore, the prime factorization of 120 is 2 × 2 × 2 × 3 × 5.
To find the prime factorization of a number, you need to determine the prime numbers that multiply together to give the given number. Here's how to find the prime factorization of 120:
1. Start by dividing the number by the smallest prime number, which is 2. 120 divided by 2 equals 60.
So, you have one factor of 2.
2. Repeat the process with the quotient obtained. Divide 60 by 2 again. This time, you get 30.
So, you have two factors of 2.
3. Continue dividing by 2 until you reach the point where the number is no longer divisible by 2.
In the case of 30, you divide it by 2 again to get 15. Now, you have three factors of 2.
4. Next, try dividing the number by the next prime number, which is 3. Divide 15 by 3, and you get 5.
So, you have one factor of 3.
5. Now, we have a prime number, which is 5. Divide 5 by 5, and you get 1.
So, you have one factor of 5.
6. Since the quotient is now 1, we can stop. The prime factors are 2 x 2 x 2 x 3 x 5, which can be written as 2^3 x 3 x 5 or simply as 2^3 * 3 * 5.
Therefore, the prime factorization of 120 is 2^3 * 3 * 5.
120: 5 x 24
24: 8 x 3
8: 2 x 4
4: 2 x 2
5 x 3 x 2 x 2 x 2