Factors of 702

The factors of 702 are the numbers that can divide 702 without leaving a remainder. These include both positive and negative factors.

Positive Factors: 1, 2, 3, 6, 9, 18, 39, 78, 117, 234, 351, 702

Negative Factors: -1, -2, -3, -6, -9, -18, -39, -78, -117, -234, -351, -702

Prime Factors: Prime factors are the prime numbers that, when multiplied together, give the original number as the product. Prime factors of 702: 2, 3, 7

Prime Factorization of 702: Prime factorization involves breaking 702 down into its prime factors, expressed as: Prime factorization of 702: 2 × 3² × 7 × 11
 

There are different methods to find the factors of 702.

Methods to Find the Factors of 702:

1. Multiplication Method
2. Division Method
3. Prime Factorization
4. Factor Tree

This breakdown helps in understanding the factors of 702, whether positive or negative, and shows how prime factorization works for this number.
 

The multiplication method involves finding pairs of numbers that, when multiplied, result in 702.

Steps:

1. Find pairs of numbers whose product is 702.
2. List all numbers that, when multiplied together, give 702.

Example List:

• 1 × 702 = 702
• 2 × 351 = 702
• 3 × 234 = 702
• 6 × 117 = 702
• 9 × 78 = 702
• 18 × 39 = 702
   

The division method involves identifying numbers that fully divide 702.

Steps:

1. Start with 1, as every number is divisible by 1 (702 ÷ 1 = 702).
2. Move to the next integer and check divisibility.
3. Include both the divisor and the quotient as factors.

Example Factors:

• 702 ÷ 1 = 702
• 702 ÷ 2 = 351
• 702 ÷ 3 = 234

Continue until all factors are found.
 

Prime factors of a number are prime numbers that multiply together to give the original number.

Finding Prime Factors of 702:

• 702 ÷ 2 = 351
• 351 ÷ 3 = 117
• 117 ÷ 3 = 39
• 39 ÷ 3 = 13
• 13 ÷ 13 = 1
•  

Prime Factorization: Prime factorization of 702 is 2 × 3³ × 13.
 

A factor tree visually represents the prime factorization of a number.

Example: The factor tree for 702 would break down as:

Each branch splits into prime factors.

Factors of 702 in Pairs

Factors of 702 can be written as pairs whose product equals 702.

Positive Factor Pairs: (1, 702), (2, 351), (3, 234), (6, 117), (9, 78), (18, 39)
Negative Factor Pairs: (-1, -702), (-2, -351), (-3, -234), (-6, -117), (-9, -78), (-18, -39)
 

• Co-prime: Numbers having 1 as the only common factor. Example: 18 and 39 are not co-prime because they share a common factor of 3.

• Perfect Square: The number we get when the same number is multiplied twice. Example: 49 is a perfect square because 7 × 7 = 49.

• Prime Factors: Prime numbers, which are factors of a given number. Example: The prime factors of 702 are 2, 3, 7, and 13.

• Factor Tree: A tree diagram used to represent the prime factors of a given number. Example: For 702, a factor tree splits into branches showing the numbers 2, 3, 3, 3, and 13.