What Are the Factors of 143 in Maths

The concept of factors of 143 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Mastering factors is especially useful in topics like divisibility, prime factorization, and finding GCF/LCM, which are all important for competitive and board exams.

Understanding Factors of 143

A factor of 143 is any whole number that divides 143 exactly, leaving no remainder. Understanding the factors of 143 is widely used in number theory, divisibility rules, and prime factorization. It also helps in comparing composite and prime numbers, and is a vital foundation for higher maths topics like LCM and HCF.

How to Find the Factors of 143

To find the factors of 143, start by dividing 143 by all numbers between 1 and 143. If your division leaves a remainder of zero, then that number is a factor. Let’s go step-by-step:

1. 143 ÷ 1 = 143

2. 143 ÷ 11 = 13

3. 143 ÷ 13 = 11

4. 143 ÷ 143 = 1

So, the factors of 143 are 1, 11, 13, and 143.

Prime Factorization of 143

Prime factorization is expressing a number as a product of its prime factors. Here’s how you can write 143 as a product of primes:

1. 143 is an odd number so it's not divisible by 2.

2. Check divisibility by 3, 5, and 7 (none divide 143).

3. Try 11: 143 ÷ 11 = 13. Both 11 and 13 are prime numbers.

Therefore, the prime factorization of 143 = 11 × 13.

Factors of 143 in Pairs

Pair factors are two numbers that multiply to give 143. Here is a clear table showing them:

Factors of 143 – Pair Table

Factor 1	Factor 2
1	143
11	13

Therefore, the pair factors of 143 are (1, 143) and (11, 13).

Properties and Divisibility of 143

143 is an odd, composite number (not prime). It is not a perfect square, as the square root of 143 (~11.96) is not a whole number. Its only prime factors are 11 and 13. It is not divisible by numbers like 2, 3, 5, or 7.

Related Numbers and Their Factors

Exploring numbers close to 143 can deepen understanding. For example, 91 (factors: 1, 7, 13, 91), 144 (factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144). You can practice factorization using such examples for exams and further revision. For prime numbers and deeper divisibility techniques, explore Prime Numbers and Fundamental Theorem of Arithmetic.

Worked Example – Solving a Problem

1. Find the sum of all factors of 143.

2. Is 143 a perfect square?

3. What is the greatest common factor (GCF) of 143 and 156?

Practice Problems

• List all factors of 143 by the division method.
• Write the prime factorization of 143.
• Is 143 a prime or composite number?
• What are the pair factors of 143?
• Find the LCM of 143 and 11.

Common Mistakes to Avoid

• Forgetting to check factors beyond 10 (like 11 and 13, both factor 143).
• Confusing factors (numbers that divide) with multiples (numbers you get by multiplying).
• Assuming 143 is a perfect square or prime without checking the definition.

Real-World Applications

The concept of factors of 143 and similar numbers appears in practical scenarios such as arranging objects in equal groups, dividing items evenly, encryption algorithms, and problem-solving in exams. Vedantu helps students link these core maths concepts to real-life and higher studies.

We explored the idea of factors of 143, how to find them, their prime factorization, pair factors, common mistakes, and their real-life relevance. With regular practice on Vedantu, you can gain complete confidence in such maths concepts for both school and competitive exams.

Explore more and practice with these related topics: Factors of 91, Factors of 144, Factors of 100, Prime Numbers, Common Factors, Fundamental Theorem of Arithmetic, Factors of a Number, Multiples of 4.