126 LearnersLast updated on May 26th, 2025
Factors of 1967
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1967, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1967?
The numbers that divide 1967 evenly are known as factors of 1967.
A factor of 1967 is a number that divides the number without remainder.
The factors of 1967 are 1 and 1967.
Negative factors of 1967: -1 and -1967.
Prime factors of 1967: 1967 itself, as it is a prime number.
Prime factorization of 1967: 1967.
The sum of factors of 1967: 1 + 1967 = 1968
How to Find Factors of 1967?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1967.
Since 1967 is a prime number, there are no pairs of numbers other than 1 and the number itself.
Therefore, the positive factor pair of 1967 is: (1, 1967).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by the following simple division method
Step 1: Divide 1967 by 1, 1967 ÷ 1 = 1967.
Step 2: Check if 1967 is divisible by any other numbers. Since 1967 is not divisible by any number other than 1 and itself, the factors of 1967 are: 1 and 1967.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. However, since 1967 is a prime number, it only has itself as its prime factor.
Using Prime Factorization: In this process, since 1967 is a prime number, the prime factorization is just 1967 itself.
Factor Tree
The factor tree is a graphical representation of breaking down any number into prime factors. Since 1967 is a prime number, the factor tree is simple and consists only of the number itself. The prime factorization of 1967 is simply 1967.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pair of 1967: (1, 1967).
Negative factor pair of 1967: (-1, -1967).
Common Mistakes and How to Avoid Them in Factors of 1967
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
People might forget to add the given number itself and 1 as factors. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1967, 1 and 1967 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1967 include -1 and -1967.
Mistake 3
Including the Fraction
Sometimes, people might mistakenly consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 1967/1.5 is not a whole number is incorrect.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all the factors of 1967 are prime numbers would be incorrect since it only has 1 and itself as factors.
Mistake 5
Mistake in Factorization
People might skip steps in factorization and end up writing incorrect factors.
For example, not recognizing 1967 as a prime number and unnecessarily trying to factorize it further.
Factors of 1967 Examples
Problem 1
A group of 1967 students needs to be divided into teams. How can they be divided into equal teams?
They can only be divided into one team of 1967 students or 1967 teams of one student each.
Explanation
Since 1967 is a prime number, it cannot be divided evenly into smaller whole number groups other than 1 and 1967 itself.
Problem 2
A charity event has 1967 chairs, and they want to arrange them in rows. What are the possible row arrangements?
They can arrange them in 1 row of 1967 chairs or 1967 rows of 1 chair each.
Explanation
Since 1967 is a prime number, it cannot be arranged in equal rows of more than 1 chair per row other than the entire set of chairs in one row.
Problem 3
A library has 1967 books and wants to categorize them equally into sections. How can they do this?
They can have 1967 sections with 1 book each or 1 section with all 1967 books.
Explanation
As 1967 is a prime number, it can only be divided into sections of size 1 or one large section.
Problem 4
A marathon has 1967 participants. How should they line up if each line should have the same number of participants?
They can line up in 1 line of 1967 participants or 1967 lines of 1 participant each.
Explanation
Because 1967 is a prime number, the only equal ways to line up are one long line or multiple lines of a single participant.
Problem 5
1967 pieces of fruit are to be packed into boxes. How many boxes can they use if each box must contain the same number of pieces?
They can use 1 box with 1967 pieces or 1967 boxes with 1 piece each.
Explanation
Being a prime number, 1967 can only be divided into equal groups of 1 or its entirety in a single group.
FAQs on Factors of 1967
1.What are the factors of 1967?
2.Mention the prime factors of 1967.
3.Is 1967 a multiple of 4?
4.Mention the factor pairs of 1967?
5.What is the square of 1967?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1967?
7.What are some fun ways kids in Qatar can practice Factors of 1967 with numbers?
8.What role do numbers and Factors of 1967 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1967 skills?
Important Glossaries for Factor of 1967
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1967 are 1 and 1967.
- Prime factors: The factors which are prime numbers. For example, 1967 is its own prime factor as it is a prime number.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 1967 is (1, 1967).
- Prime number: A number greater than 1 that has no divisors other than 1 and itself. For example, 1967 is a prime number.
- Prime factorization: The expression of a number as the product of its prime factors. In the case of 1967, it is 1967 itself.
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About BrightChamps in Qatar
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.
