Factors of 720720

The numbers that divide 720720 evenly are known as factors of 720720. A factor of 720720 is a number that divides the number without remainder. The factors of 720720 include 1, 2, 3, 4, 5, 6, and many others.

Negative factors of 720720: -1, -2, -3, -4, -5, -6, and many others.

Prime factors of 720720: 2, 3, 5, 7, 11, and 13.

Prime factorization of 720720: 2⁴ × 3² × 5 × 7 × 11 × 13.

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 720720. Identifying the numbers which are multiplied to get the number 720720 is the multiplication method.

Step 1: Multiply 720720 by 1, 720720 × 1 = 720720.

Step 2: Check for other numbers that give 720720 after multiplying. For instance:

2 × 360360 = 720720

3 × 240240 = 720720

5 × 144144 = 720720

6 × 120120 = 720720

Therefore, the positive factor pairs of 720720 include: (1, 720720), (2, 360360), (3, 240240), (5, 144144), (6, 120120). For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 720720 by 1, 720720 ÷ 1 = 720720.

Step 2: Continue dividing 720720 by the numbers until the remainder becomes 0.

For example:

720720 ÷ 1 = 720720

720720 ÷ 2 = 360360

720720 ÷ 3 = 240240

720720 ÷ 5 = 144144

720720 ÷ 6 = 120120

Therefore, the factors of 720720 include: 1, 2, 3, 5, 6, and many more.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 720720 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

720720 ÷ 2 = 360360

360360 ÷ 2 = 180180

180180 ÷ 2 = 90090

90090 ÷ 2 = 45045

45045 ÷ 3 = 15015

15015 ÷ 3 = 5005

5005 ÷ 5 = 1001

1001 ÷ 7 = 143

143 ÷ 11 = 13

13 ÷ 13 = 1

The prime factors of 720720 are 2, 3, 5, 7, 11, and 13. The prime factorization of 720720 is: 2⁴ × 3² × 5 × 7 × 11 × 13.

The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -

Step 1: Firstly, 720720 is divided by 2 to get 360360.

Step 2: Now divide 360360 by 2 to get 180180.

Step 3: Then divide 180180 by 2 to get 90090.

Step 4: Divide 90090 by 2 to get 45045.

Step 5: Divide 45045 by 3 to get 15015.

Step 6: Divide 15015 by 3 to get 5005.

Step 7: Divide 5005 by 5 to get 1001.

Step 8: Divide 1001 by 7 to get 143. Step 9: Divide 143 by 11 to get 13. 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 720720 is: 2⁴ × 3² × 5 × 7 × 11 × 13.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 720720 include: (1, 720720), (2, 360360), (3, 240240), etc.

• Negative factor pairs of 720720 include: (-1, -720720), (-2, -360360), (-3, -240240), etc.

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 720720 include 1, 2, 3, 5, 6, and many more.

• Prime factors: The factors which are prime numbers. For example, 2, 3, 5, 7, 11, and 13 are prime factors of 720720.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 720720 include (1, 720720), (2, 360360), etc.

• Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 720720 is 2⁴ × 3² × 5 × 7 × 11 × 13.

• Divisors: Numbers that divide another number completely without leaving a remainder. For instance, the divisors of 720720 include 1, 2, 3, 4, etc.