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Factors of 702

Factors of 702 are numbers that, when multiplied in pairs give the product as 702. There are overall 16 factors of 702, of which 2, 3, 13 are its prime factors. The sum of all factors of 702 is 1680.

All Factors of 702: 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351 and 702
Prime Factors of 702: 2, 3, 13
Prime Factorization of 702: 2¹ × 3³ × 13¹
Sum of Factors of 702: 1680

1.	What Are the Factors of 702?
2.	Factors of 702 by Prime Factorization
3.	Factors of 702 in Pairs
4.	FAQs on Factors of 702

What are Factors of 702?

Factors of 702 are pairs of those numbers whose products result in 702. These factors are either prime numbers or composite numbers.

How to Find the Factors of 702?

To find the factors of 702, we will have to find the list of numbers that would divide 702 without leaving any remainder.

702/3 = 234; therefore, 3 is a factor of 702 and 234 is also a factor of 702.
702/18 = 39; therefore, 18 is a factor of 702 and 39 is also a factor of 702.

Similarly we can find other factors. Hence, the factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.

☛ Also Check:

Factors of 37 - The factors of 37 are 1, 37
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 23 - The factors of 23 are 1, 23
Factors of 15 - The factors of 15 are 1, 3, 5, 15

Factors of 702 by Prime Factorization

The number 702 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 702. The first step is to divide the number 702 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

702 ÷ 2 = 351

Further dividing 351 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 351 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 702 can be written as 2¹ × 3³ × 13¹ where 2, 3, 13 are prime.

Factors of 702 in Pairs

Pair factors of 702 are the pairs of numbers that when multiplied give the product 702. The factors of 702 in pairs are:

1 × 702 = (1, 702)
2 × 351 = (2, 351)
3 × 234 = (3, 234)
6 × 117 = (6, 117)
9 × 78 = (9, 78)
13 × 54 = (13, 54)
18 × 39 = (18, 39)
26 × 27 = (26, 27)

Negative pair factors of 702 are:

-1 × -702 = (-1, -702)
-2 × -351 = (-2, -351)
-3 × -234 = (-3, -234)
-6 × -117 = (-6, -117)
-9 × -78 = (-9, -78)
-13 × -54 = (-13, -54)
-18 × -39 = (-18, -39)
-26 × -27 = (-26, -27)

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

Factors of 702 Solved Examples

Example 1: How many factors are there for 702?

Solution:

The factors of 702 are too many, therefore if we can find the prime factorization of 702, 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 702 = 2¹ × 3³ × 13¹
Therefore, the total number of factors are (1 + 1) × (3 + 1) × (1 + 1) = 2 × 4 × 2 = 16
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 702 and 431.

Solution:

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702 and factors of 431 are 1, 431.

Therefore, the Least Common Multiple of 702 and 431 is 302562 and Greatest Common Divisor (GCD) of 702 and 431 is 1.
Example 3: Find if 1, 3, 6, 9, 27, 42, 54 and 351 are factors of 702.

Solution:

When we divide 702 by 42 it leaves a remainder. Therefore, the number 42 is not a factor of 702. All numbers except 42 are factors of 702.
Example 4: Find the product of all the prime factors of 702.

Solution:

Since, the prime factors of 702 are 2, 3, 13. Therefore, the product of prime factors = 2 × 3 × 13 = 78.

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FAQs on Factors of 702

What are the Factors of 702?

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702 and its negative factors are -1, -2, -3, -6, -9, -13, -18, -26, -27, -39, -54, -78, -117, -234, -351, -702.

What is the Sum of Factors of 702?

Sum of all factors of 702 = (2^{1 + 1} - 1)/(2 - 1) × (3^{3 + 1} - 1)/(3 - 1) × (13^{1 + 1} - 1)/(13 - 1) = 1680

What are Prime Factors of 702?

The prime factors of 702 are 2, 3, 13.

What is the Greatest Common Factor of 702 and 475?

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702 and the factors of 475 are 1, 5, 19, 25, 95, 475. 702 and 475 have only one common factor which is 1. This implies that 702 and 475 are co-prime.

Hence, the Greatest Common Factor (GCF) of 702 and 475 is 1.

What are the Common Factors of 702 and 29?

Since, the factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702 and factors of 29 are 1, 29. Hence, 702 and 29 have only one common factor which is 1. Therefore, 702 and 29 are co-prime.

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