171 LearnersLast updated on May 26th, 2025
Factors of 702
Factors of 702 are numbers that can divide 702 completely without any remainder. We often use factors in practical scenarios such as organizing events and seating arrangements. In this topic, we will explore the factors of 702 and the different methods to find them.
What are the 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
How to Find the Factors of 702?
There are different methods to find the factors of 702.
Methods to Find the Factors of 702:
- Multiplication Method
- Division Method
- Prime Factorization
- Factor Tree
This breakdown helps in understanding the factors of 702, whether positive or negative, and shows how prime factorization works for this number.
Finding Factors Using Multiplication
The multiplication method involves finding pairs of numbers that, when multiplied, result in 702.
Steps:
- Find pairs of numbers whose product is 702.
- 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
Finding Factors by Division Method
The division method involves identifying numbers that fully divide 702.
Steps:
- Start with 1, as every number is divisible by 1 (702 ÷ 1 = 702).
- Move to the next integer and check divisibility.
- 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 and Prime Factorization
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.
Factor Tree
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)
Common Mistakes and How to Avoid Them in Factors of 702
Mistakes can occur when identifying factors. Below are common errors and their solutions.
Mistake 1
Assuming only the smallest factors are correct
Always check all numbers up to the square root of the given number to identify all factors
Factors of 702 Examples
Problem 1
Can you check whether 18 and 39 are co-prime?
No, 18 and 39 are not co-prime
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 39: 1, 3, 13, 39
Here, the GCF is 3. So, 18 and 39 are not co-prime. For co-prime, the GCF of numbers should be 1
Problem 2
Verify whether 702 is a multiple of 9
Yes, 702 is a multiple of 9
Explanation
Multiples of 9 are numbers we get when 9 is multiplied by another number. Since 702 ÷ 9 = 78 with no remainder, 702 is a multiple of 9.
Problem 3
Identify the perfect square from the factors of 702
The perfect square factor of 702 is 49 and the root is 7
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 7 is multiplied twice (7×7) we get the perfect square 49.
Problem 4
What are the factors of 702?
The factors of 702 are 1, 2, 3, 6, 9, 14, 18, 21, 26, 27, 42, 51, 78, 102, 126, 154, 189, 252, 378, 702
Explanation
To find the factors of 702, divide it by all numbers from 1 up to 702 and include the numbers that divide evenly without a remainder.
Problem 5
Can you check if 26 and 39 are co-prime?
No, 26 and 39 are not co-prime
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 26: 1, 2, 13, 26
Factors of 39: 1, 3, 13, 39
Here, the GCF is 13. So, 26 and 39 are not co-prime. For co-prime, the GCF of numbers should be 1.
FAQs on Factors of 702
1.What are the factors of 702?
2.How do you determine if a number is a factor of 702?
3.What is the smallest factor of 702?
4.What is the largest factor of 702?
5.How many factors does 702 have?
6.How many odd factors does 702 have?
7.What factors go into 702?
Important glossaries for the Factors of 702
- 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.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
