Factors of 62 Explained: Definition, List, Prime Factors & Pairs

The concept of factors of 62 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding factors helps students master problems on divisibility, HCF, LCM, and number properties. Let's learn everything you need to know about the factors of 62 in an easy, step-by-step manner.

What Is Factors of 62?

A factor of 62 is any integer that divides 62 exactly without leaving any remainder. In simple terms, factors are whole numbers you can multiply in pairs to get 62. You’ll find this concept applied in areas such as divisibility rules, prime factorization, and when finding HCF or LCM in Maths. Similarly, factors play a big role in algebra and data analysis too.

Key Formula for Factors of 62

Here’s the standard formula: If a is a factor of 62, then \( 62 \div a = \text{Integer with remainder 0} \).
For example: \( 62 \div 2 = 31 \), which is also a factor.

How to Find Factors of 62

To find all the factors of 62, check each number from 1 up to 62. If the result is a whole number, you’ve found a factor.

Divisor	Result	Is Factor?
1	62 ÷ 1 = 62	Yes
2	62 ÷ 2 = 31	Yes
31	62 ÷ 31 = 2	Yes
62	62 ÷ 62 = 1	Yes

So, the factors of 62 are 1, 2, 31, and 62. Negative factors (−1, −2, −31, −62) also exist since multiplying two negatives gives a positive product.

Pair Factors of 62

Pair factors are two numbers which multiply to give 62. These pairs help you visualize factors easily.

Pair	Product
(1, 62)	1 × 62 = 62
(2, 31)	2 × 31 = 62
(-1, -62)	-1 × -62 = 62
(-2, -31)	-2 × -31 = 62

Prime Factorization of 62

Prime factorization means expressing 62 as the product of its smallest prime factors. Let’s use the step-by-step method:

1. Divide 62 by the smallest prime (2):
   
   62 ÷ 2 = 31
2. Check if 31 is a prime number:
   
   31 cannot be divided by primes less than itself (other than 1 and 31) — so it is prime.
3. Therefore, 62 = 2 × 31

So, the prime factors of 62 are 2 and 31. This is useful for finding HCF, LCM, and simplifying algebraic problems.

Properties and Divisibility of 62

• 62 is an even composite number.
• Total factors: Four (1, 2, 31, 62).
• Sum of all factors: 1 + 2 + 31 + 62 = 96.
• Is 2 a factor? Yes, as 62 is divisible by 2.
• All factors of 62 are integers; there are no fractional or decimal factors.

Step-by-Step Example: Common Factors and HCF

Let’s solve an exam-style problem using factors of 62 step by step:

1. Question: What is the HCF of 62 and 70?

2. Find prime factors of 62: 2 × 31.

3. Find prime factors of 70: 2 × 5 × 7.

4. List common prime factors: Only 2 is common.

5. Final Answer: HCF = 2.

Try These Yourself

• What are the prime factors of 31?
• List all factors of 64 and compare with factors of 62.
• Find the sum of all positive factors of 62.
• Which of the following are factors of 62: 2, 3, 31, 32?
• What is the LCM of 62 and 31?

Frequent Errors and Misunderstandings

• Forgetting to include both 1 and 62 as factors.
• Confusing factors with multiples.
• Assuming every even number is a factor of 62 (not true; for example, 4 is not a factor of 62).
• Missing negative factors in advanced classes.

Relation to Other Concepts

The idea of factors of 62 connects directly to Prime Factorization, LCM and HCF, and Common Factors. Mastering this topic helps students tackle more complex number theory and algebra problems.

Classroom Tip

A quick way to remember factors of any number is to check divisibility starting from 1 upwards and noting both members of each pair (like 2 and 31). Vedantu’s teachers use visual aids like factor trees to make these patterns easier to spot in class.

We explored factors of 62—definition, finding steps, prime factorization, tables, exam examples, and mistakes to avoid. For deeper understanding and more practice, check out Vedantu’s lessons on factors of 60 and factors of 64. Keep practicing with Vedantu to become confident in solving all factor-related questions!