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Factors of 736

Factors of 736 are the list of integers that we can split evenly into 736. There are overall 12 factors of 736 among which 736 is the biggest factor and its prime factors are 2, 23. The sum of all factors of 736 is 1512.

All Factors of 736: 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368 and 736
Prime Factors of 736: 2, 23
Prime Factorization of 736: 2⁵ × 23¹
Sum of Factors of 736: 1512

1.	What Are the Factors of 736?
2.	Factors of 736 by Prime Factorization
3.	Factors of 736 in Pairs
4.	FAQs on Factors of 736

What are Factors of 736?

Factors of 736 are pairs of those numbers whose products result in 736. These factors are either prime numbers or composite numbers.

How to Find the Factors of 736?

To find the factors of 736, we will have to find the list of numbers that would divide 736 without leaving any remainder.

736/92 = 8; therefore, 92 is a factor of 736 and 8 is also a factor of 736.
736/46 = 16; therefore, 46 is a factor of 736 and 16 is also a factor of 736.

Similarly we can find other factors. Hence, the factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.

☛ Also Check:

Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 66 - The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98

Factors of 736 by Prime Factorization

The number 736 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 736. The first step is to divide the number 736 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

736 ÷ 2 = 368
368 ÷ 2 = 184
184 ÷ 2 = 92
92 ÷ 2 = 46
46 ÷ 2 = 23

Further dividing 23 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 23 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 736 can be written as 2⁵ × 23¹ where 2, 23 are prime.

Factors of 736 in Pairs

Pair factors of 736 are the pairs of numbers that when multiplied give the product 736. The factors of 736 in pairs are:

1 × 736 = (1, 736)
2 × 368 = (2, 368)
4 × 184 = (4, 184)
8 × 92 = (8, 92)
16 × 46 = (16, 46)
23 × 32 = (23, 32)

Negative pair factors of 736 are:

-1 × -736 = (-1, -736)
-2 × -368 = (-2, -368)
-4 × -184 = (-4, -184)
-8 × -92 = (-8, -92)
-16 × -46 = (-16, -46)
-23 × -32 = (-23, -32)

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

Factors of 736 Solved Examples

Example 1: How many factors are there for 736?

Solution:

The factors of 736 are too many, therefore if we can find the prime factorization of 736, 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 736 = 2⁵ × 23¹
Therefore, the total number of factors are (5 + 1) × (1 + 1) = 6 × 2 = 12
Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 736 and 699.

Solution:

The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736 and factors of 699 are 1, 3, 233, 699.

Therefore, the Least Common Multiple of 736 and 699 is 514464 and Greatest Common Factor (GCF) of 736 and 699 is 1.
Example 3: Find if 1, 4, 8, 32, 368, 618 and 736 are factors of 736.

Solution:

When we divide 736 by 618 it leaves a remainder. Therefore, the number 618 is not a factor of 736. All numbers except 618 are factors of 736.
Example 4: Find the product of all the prime factors of 736.

Solution:

Since, the prime factors of 736 are 2, 23. Therefore, the product of prime factors = 2 × 23 = 46.

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FAQs on Factors of 736

What are the Factors of 736?

The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736 and its negative factors are -1, -2, -4, -8, -16, -23, -32, -46, -92, -184, -368, -736.

What is the Sum of the Factors of 736?

Sum of all factors of 736 = (2^{5 + 1} - 1)/(2 - 1) × (23^{1 + 1} - 1)/(23 - 1) = 1512

What are the Pair Factors of 736?

The pair factors of 736 are (1, 736), (2, 368), (4, 184), (8, 92), (16, 46), (23, 32).

What is the Greatest Common Factor of 736 and 677?

The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736 and the factors of 677 are 1, 677. 736 and 677 have only one common factor which is 1. This implies that 736 and 677 are co-prime.

Hence, the Greatest Common Factor (GCF) of 736 and 677 is 1.

How Many Factors of 736 are also Factors of 255?

Since, the factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736 and factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255. Hence, 736 and 255 have only one common factor which is 1. Therefore, 736 and 255 are co-prime.

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