Factors of 62: An Introduction
The numbers that divide 62 evenly without producing a remainder are known as the factors of 62. It is possible to represent the factors and pair factors of 62 in both positive and negative forms but not in decimal or fractional forms. The pair factors of 62 are shown as (1, 62) or (-1, -62). When two negative numbers are multiplied, for example, -2 and -31, the result is 62.
This article will cover the factors of 62, the positive and negative pair factors of 62, and how to use the prime factorisation method to discover the prime factors of 62.
What are the Factors of 62?
The factors of 62 are the integers that divide 62 evenly and have a remainder of 0. In other words, the factors of 62 are the integers that, when multiplied in pairs, result in the original number 62. 62 is an even composite number; therefore, it has more than two factors. Hence, 1, 2, 31, and 62 are the factors of 62. Similarly, -1, -2, -31, and -62 are the negative components of 62.
Factors of 62 are 1, 2, 31, 62, -1,-2, -31,-62.
Prime Factorization of 62
The number 62 is represented as the product of its prime components when it is divided into its prime factors. Find the prime factors of 62 by following the steps below.
Step 1: Divide 62 by the smallest prime number 2
\[62 \div 2 = 31\]
Step 2: Check whether 31 is divisible by the next prime:
31 is an odd number so it is not divisible by 2.
3 + 1 = 4 which is not divisible by 3. Thus 31 is not divisible by 3.
31 is an odd number so it is not divisible by any even number.
31 is not divisible by any odd number, since 31 is a prime number. Thus it is divisible by 1 and itself.
So, \[62 = 2 \times 31\].
Prime Factors of 62
Prime numbers are those with just two components, namely 1 and the number itself. The factors of 62 are 1, 2, 31, and 62. The prime numbers among these are 2 and 31. In this case, 2 and 31 are 62's prime factors.
Pair Factors of 62
The pair factors of 62 are the two numbers that, when multiplied together, equal the number 62. The pair factors of 62 that are positive and negative are as follows.
Hence, the positive pairs of 62 are (1, 62) and (2,31). The negative pairs of 62 are (-1, -62) and (-2, -31).
Factors of 62 by Division Method
The division method can be used to find the elements of 62. The number 62 can be divided in this way by several integers. The integers are the factors of 62 if they divide 62 evenly and without leaving a residue. Let's discuss how to divide 62 to discover its factors using the division method.
\[\dfrac{62}{1} = 62\] (Remainder is 0)
\[\dfrac{62}{2} = 31\] (Remainder is 0)
\[\dfrac{62}{31} = 2\] (Remainder is 0)
\[\dfrac{62}{62} = 1\] (Remainder is 0)
Try to divide 62 with any other integers. You will not receive a quotient with a remainder of 0. Hence through this method, the factors of 62 are found as 1, 2, 31, and 62.
Interesting Facts
1 is neither a prime nor a composite number.
A composite number has more than two positive factors.
Solved examples
1: What is the HCF of 62 and 70?
Solution: Initially, find the prime factors of 62 and 70.
Prime factors of 62 are 2, 31. Prime factorisation of 62 is done below:
62 = 2 × 31
Prime factors of 70 are 2, 5, 7. Prime factorisation of 70 is done below:
70 = 2 × 5 × 7
The HCF is the highest common factor of the two numbers. Here, the highest common factor between 62 and 70 is 2. Hence the HCF of 62 and 70 is 2.
2: Find the common factors of 62 and 31.
Solution: Here, the factors of 62 are 1, 2, 31 and 62.
The factors of 31 are 31 and 1.
Hence, the common factor of 62 and 31 is 1 and 31.
3: What is the sum of all factors of 62?
Solution: Here, the factors of 62 are 1, 2, 31 and 62.
Sum = 1 + 2 + 31 + 62 = 96
Hence, the sum of all factors of 62 is 96.
4: Find the common factors of 62 and 100.
Solution: Here, the factors of 62 are 1, 2, 31 and 62.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Hence, the common factor of 62 and 100 are 1 and 2.
Conclusion
In this topic page, we have learned about the factors of 62, all the factors of 62, its prime factorisation, prime factors of 62 and factor pairs of 62.
Key Features
To find the factors of 62, we can use the division method.
The factors of 62 are 1, 2, 31, 62 and their negative counterparts.
The factor pairs of 62 are \[1\times 62\], \[2\times 31\], \[-1\times -62\] and \[-2\times-31\]
Practice Problems
1. What are the prime factors of 34?
Answer: 2 and 17.
2. What is the sum of all factors of 34?
Answer: 0
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FAQs on Factors of 62
1. Is 54 a factor of 62?
No, 54 is not a factor of 62. If 62 is divided by 54, it leaves a quotient of 1 and a remainder of 8, and hence, 54 is not a factor of 62.
2. Is 62 composite or prime number?
62 has four factors, which are 1, 2, 31 and 62. So 62 has factors other than 1 and 62. Hence, 62 is a composite number.
3. What are the different factors of 62?
The factors of 62 are 1,2,31, and 62. Hence, different factorisations of 62 are 1 × 62, and 2 × 31.
4. What are the negative pair factors of 62?
The negative factors of 62 are -1, -62, -2 and -31. Hence, the negative pairs of 62 are (-1, -62) and (-2, -31).