Factors of 62 Using Prime Factorization
What are the Factors of 62?
If the number 62 is divided by a natural number such that the remainder is zero, the natural number is known as a factor of 62. Here, the quotient obtained on division is also a factor of 62.
The factors of 62 are 1, 2, 31, and 62 because all these numbers divide the number 62 evenly.
List of the Factors of 62
Divisibility rules and division facts can be applied to determine the factors of 62.
If we continue the same way, we will notice that the number will repeat on reaching 31. Hence, we can stop checking the factor pairs after 31 as they begin to repeat.
So, the factors of 62 are 1, 2, 31, and 62.
[Note: If we divide 62 by 35, we get the quotient and remainder as 1 and 27, respectively. So, 35 is not a factor of 62. Similarly, you can check for other numbers as well.]
The Prime Factorization of 62
If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that natural number. The process of writing this multiplication of prime factors is known as prime factorization.
The prime factorization of 62 can be represented by using a factor tree as shown below.
So, the prime factorization of 62 is 62 = 2 \(\times\) 31, and the prime factors of 62 are 2 and 31.
Factor Pairs of 62
A factor pair of a number is a set of any of its two factors such that their product is the number itself. A factor pair can be negative or positive.
The positive factor pairs of 62 are (1, 62) and (2, 31).
1 \(\times\) 62 = 62
2 \(\times\) 31 = 62
Read More:
Positive Factor Pairs of 62
Positive Factors of 62 | Positive Factor Pairs of 62 |
|---|---|
1 × 62 | (1, 62) |
2 × 31 | (2, 31) |
Rapid Recall
The factors of 62 are 1, 2, 31, and 62
Solved Factors of 62 Examples
Example 1: Find the common factors of 26 and 62.
Solution:
Factors of 26 = 1, 2, 13, and 26
Factors of 62 = 1, 2, 31, and 62
Therefore, the common factors of 26 and 62 are 1 and 2.
Example 2: Find the greatest common factor of 62 and 60.
Solution:
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 62 = 1, 2, 31, and 62.
So, the common factors of 60 and 62 are 1 and 2.
Therefore, the greatest common factor of 60 and 62 is 2.
Example 3: What is the sum of the prime factors of 62?
Solution:
Factors of 62 are 1, 2, 31, and 62.
So, prime factors of 62 are 2 and 31.
Therefore, sum of prime factors of 62 are 2 + 31 = 33.
Example 4: John was studying geometrical shapes and found a triangle of area 31 square centimeters. What are the possible dimensions of the base and height of the triangle?
Solution :
The area of triangle
= \(\frac{1}{2}\times b \times h\) Where b is base and h is height.
31 = \(\frac{1}{2}\times b \times h\) Area of the triangle is 31 sq.cm.
62 = \(b \times h\) Multiply both sides by 2.
So, the dimensions of the triangle will be the factor pairs of 62, which are, (1, 62), (2, 31), (31, 2) and (62, 1)
Therefore, the possible dimensions of the triangle are:
Composite numbers are numbers that have more than two factors.
The division of any positive number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all positive numbers.
Factors of 62 are 1, 2, 31, and 62.
So, prime factors of 62 are 2 and 31.
Therefore, product of prime factors of 62 is 2\(\times\) 31 = 62.
The factors of 62 are the numbers that divide 62 exactly, with the remainder as zero. The number 62 is exactly divisible by 1, 2, 31, and 62. So, the factors of 62 are 1, 2, 31, and 62.