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Factors of 726

Factors of 726 are numbers that, when multiplied in pairs give the product as 726. There are total 12 factors of 726, of which 2, 3, 11 are its prime factors. The sum of all factors of 726 is 1596.

All Factors of 726: 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363 and 726
Prime Factors of 726: 2, 3, 11
Prime Factorization of 726: 2¹ × 3¹ × 11²
Sum of Factors of 726: 1596

1.	What Are the Factors of 726?
2.	Factors of 726 by Prime Factorization
3.	Factors of 726 in Pairs
4.	FAQs on Factors of 726

What are Factors of 726?

Factors of 726 are pairs of those numbers whose products result in 726. These factors are either prime numbers or composite numbers.

How to Find the Factors of 726?

To find the factors of 726, we will have to find the list of numbers that would divide 726 without leaving any remainder.

726/11 = 66; therefore, 11 is a factor of 726 and 66 is also a factor of 726.
726/363 = 2; therefore, 363 is a factor of 726 and 2 is also a factor of 726.

Similarly we can find other factors. Hence, the factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.

☛ Also Check:

Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28
Factors of 4 - The factors of 4 are 1, 2, 4
Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 91 - The factors of 91 are 1, 7, 13, 91
Factors of 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Factors of 726 by Prime Factorization

The number 726 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 726. The first step is to divide the number 726 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

726 ÷ 2 = 363

Further dividing 363 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 363 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 726 can be written as 2¹ × 3¹ × 11² where 2, 3, 11 are prime.

Factors of 726 in Pairs

Pair factors of 726 are the pairs of numbers that when multiplied give the product 726. The factors of 726 in pairs are:

1 × 726 = (1, 726)
2 × 363 = (2, 363)
3 × 242 = (3, 242)
6 × 121 = (6, 121)
11 × 66 = (11, 66)
22 × 33 = (22, 33)

Negative pair factors of 726 are:

-1 × -726 = (-1, -726)
-2 × -363 = (-2, -363)
-3 × -242 = (-3, -242)
-6 × -121 = (-6, -121)
-11 × -66 = (-11, -66)
-22 × -33 = (-22, -33)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 726 Solved Examples

Example 1: How many factors are there for 726?

Solution:

The factors of 726 are too many, therefore if we can find the prime factorization of 726, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 726 = 2¹ × 3¹ × 11²
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (2 + 1) = 2 × 2 × 3 = 12
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 726 and 643.

Solution:

The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726 and factors of 643 are 1, 643.

Therefore, the Lowest Common Multiple (LCM) of 726 and 643 is 466818 and Greatest Common Divisor (GCD) of 726 and 643 is 1.
Example 3: Find if 3, 11, 22, 33, 121, 242 and 638 are factors of 726.

Solution:

When we divide 726 by 638 it leaves a remainder. Therefore, the number 638 is not a factor of 726. All numbers except 638 are factors of 726.
Example 4: Find the product of all the prime factors of 726.

Solution:

Since, the prime factors of 726 are 2, 3, 11. Therefore, the product of prime factors = 2 × 3 × 11 = 66.

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FAQs on Factors of 726

What are the Factors of 726?

The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726 and its negative factors are -1, -2, -3, -6, -11, -22, -33, -66, -121, -242, -363, -726.

What is the Sum of all Factors of 726?

Sum of all factors of 726 = (2^{1 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (11^{2 + 1} - 1)/(11 - 1) = 1596

What are Prime Factors of 726?

The prime factors of 726 are 2, 3, 11.

What is the Greatest Common Factor of 726 and 176?

The factors of 726 and 176 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726 and 1, 2, 4, 8, 11, 16, 22, 44, 88, 176 respectively.

Common factors of 726 and 176 are [1, 2, 11, 22].

Hence, the Greatest Common Factor (GCF) of 726 and 176 is 22.

How Many Factors of 34 are also common to the Factors of 726?

Since, the factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726 and the factors of 34 are 1, 2, 17, 34.
Hence, [1, 2] are the common factors of 726 and 34.

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