How to Draw a Factor Tree for 72
Factors of 72
Factors of 72 are the list of integers that can be evenly divided into 72. There are overall 12 factors of 72 among which 72 is the biggest factor and 2 and 3 are its prime factors. The sum of all factors of 72 is 195.
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
- Negative Factors of 72: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36 and -72
- Prime Factors of 72: 2, 3
- Prime Factorization of 72: 2 × 2 × 2 × 3 × 3 = 23 × 32
- Sum of Factors of 72: 195
| 1. | What are Factors of 72? |
| 2. | How to Calculate the Factors of 72? |
| 3. | Tips and Tricks |
What are Factors of 72?
- Factors of 72 are numbers which, on dividing 72, leave no remainder.
- Since 72 is a composite number, it has more than two factors.
- We can use division to check whether 4, 18, and 24 are factors of 72. As they leave no remainder, they are indeed the factors of 72!
- 72 has a total of 12 factors: 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.
How to Calculate the Factors of 72?
Factorization of a number means writing the number as a product of its factors. There are two common methods to find the factors of 72.
1. Division method
2. Prime factorization method
Let us calculate factors of 72 using the division method. In considering numbers that can divide 72 without remainders, we start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 36 (which is exactly half of 72).
| 72 ÷ 1 = 72 |
| 72 ÷ 2 = 36 |
| 72 ÷ 3 = 24 |
| 72 ÷ 4 = 18 |
| 72 ÷ 6 = 12 |
| 72 ÷ 8 = 9 |
| 72 ÷ 9 = 8 |
| 72 ÷ 12 = 6 |
| 72 ÷ 18 = 4 |
| 72 ÷ 24 = 3 |
| 72 ÷ 36 = 2 |
| 72 ÷ 72 = 1 |
All these divisors 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 form the factors of 72 as when divided, they have no remainders.
Tips and Tricks
- 72 = 2 × 2 × 2 × 3 × 3 = \(2 ^3 \times 3 ^2\). Just add one to the exponents 3 and 2 individually and multiply their sums. (3 +1) × (2 +1) = 4 × 3 = 12. This gives the total number of factors of 72.
- Use prime factorization, get the prime factors of 72 and multiply them in all possible ways to get all the 12 factors listed as 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.
Factors of 72 by Prime Factorization
Prime factorization is to express a composite number as the product of its prime factors.
- Step 1: The first step is to divide the number 72 with the smallest prime factor, say 2.
72 ÷ 2 = 36 - Step 2: Divide 36 again by 2.
36 ÷ 2 = 18 - Step 3: Divide 18 again by 2.
18 ÷ 2 = 9 - Step 4: 9 ÷ 2 = 4.5. Now if we divide 9 by 2, we get a fractional number and a factor cannot be a fraction or a decimal number. So, proceed with the next prime factor, say 3.
That is 9 ÷ 3 = 3 - Step 5: Similarly, 3 ÷ 3 = 1
- Step 6: We cannot proceed further as we have obtained 1 as our quotient.
- Step 7: The prime factors of 72 are written as 2 × 2 × 2 × 3 × 3,= \(2 ^3 \times 3 ^2\), where 2 and 3 are the prime numbers.
We can also find the prime factors using a factor tree. The ends of a factor tree are all the prime factors of the original number.
There is more than one way of making a factor tree. Here are some more factor trees of the same number 72:
- The prime factors are encircled in the factor tree.
- So, the prime factors of 72 are written as 72 = 2 × 2 × 2 × 3 × 3.
- Now that we have done the prime factorization of 72, we can multiply them and get all the other composite factors.
Explore factors using illustrations and interactive examples.
- Factors of 96 : The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360
- Factors of 12: The factors of 12 are 1, 2, 3, 4, 6, 12
- Factors of 48 : The factors of 48 are 1, 2, 3, 4, 6, 8,12,16, 24, 48
Factors of 72 in Pairs
- Pair factors of the number 72 are whole numbers in pairs that multiply to get the original number, i.e., 72.
- Pair factors could be either positive or negative but not a fraction or a decimal number.
- There are 12 pair factors of 72 and they are as follows: (1, 72), (-1, -72), (2, 36), (-2, -36), (3, 24), (-3, -24), (4, 18), (-4, -18), (6, 12), (-6, -12), (8, 9), and (-8, -9)
Important Notes
- Only whole numbers and integers can be converted to factors.
- Only composite numbers can have more than two factors
- Every factor of a given number is either less than or equal to the given number.
- The number of factors of a given number is finite. 72 has 12 factors.
Factors of 72 Solved Examples
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FAQs on Factors of 72
What are the Factors of 72?
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, -72.
What is the Sum of all the Factors of 72?
Sum of all factors of 72 = (23 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) = 195
How Many Factors of 72 are also common to the Factors of 19?
Since, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and factors of 19 are 1, 19. Hence, 72 and 19 have only one common factor which is 1. Therefore, 72 and 19 are co-prime.
What are the Pair Factors of 72?
The pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9).
What is the Greatest Common Factor of 72 and 63?
The factors of 72 and 63 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 3, 7, 9, 21, 63 respectively.
Common factors of 72 and 63 are [1, 3, 9].
Hence, the GCF of 72 and 63 is 9.
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Source: https://www.cuemath.com/numbers/factors-of-72/#:~:text=The%20prime%20factors%20are%20encircled,2%20%C3%97%203%20%C3%97%203.