Factors of 67
When you try and find the factors of a prime number, you will always get 1 and that number as the factors. This is the fundamental rule of a prime number. Did you know that the number 67 is the 19th prime number? Also, the sum of the following five consecutive primes (7+11+13+17+19) is 67. These factors can be negative as well. In this lesson, we will calculate the factors of 67, prime factors of 67, and factors of 67 in pairs along with solved examples for a better understanding.
Factors of 67: 1, 67.
Prime Factorization of 67: 67 = 1 x 67
|1.||What Are the Factors of 67?|
|2.||How to Calculate the Factors of 67?|
|4.||Factors of 67 in Pairs|
|5.||Factors of 67 by Prime Factorization|
|6.||FAQs on Factors of 67|
What Are the Factors of 67?
Factors of 67 are the numbers which, when multiplied in pairs, give the product as 67. The number 67 falls in the category of prime numbers. A prime number is only divisible by 1 and by the same number itself. Here, the factors of 67 are 1 and 67. Hence, 67 is a prime number.
How to Calculate the Factors of 67?
The next whole number is 2. But since 67 is an odd number, all of its factors will also be odd. We will try with number 3.
- 67 ÷ 3 = 22.33…
Here, 3 is not a factor. Proceeding in a similar manner, we calculated the factors of 67, i.e., 1 and 67.
- As the number 67 is an odd prime number, all of its factors will also be odd.
- Factors of 67 are 1 and 67.
- 1 is a universal factor since it is a factor of all numbers.
Factors of 67 in pairs
The pair of numbers which gives 67 when multiplied is called pair factors of 67. As discussed earlier, 67 is a prime number, which has only two factors. Therefore, 67 has only one pair factor, i.e., (1, 67). Using this, negative pair factors of 67 can also be found. They are (-1, -67).
Factors of 67 by Prime Factorization
Prime factorization means expressing a number in terms of the product of its prime factors. The process of prime factorization goes on till we get the quotient as 1. The process always starts with the smallest prime factor.
As per the definition, itcan also be written as 67 = 67 × 1.
Solved Examples on Factors of 67
Example 1 Can you find the common factors of 67 and 134?
Factors of 67 by prime factorization are 1 and 67, and factors of 134 by prime factorization are 1, 67, and 134.
Hence, the common factors of 67 and 134 are 1 and 67.
Example 2 Help Sam to find the factors of 67, which are less than 10, from cards having numbers written less than 10.
Factors of 67 are 1 and 67.
But Sam is asked to pick the factor less than 10
Hence, 1 is the factor of 67, which is less than 10.
FAQs on factors of 67
What are the factors of 67?
The factors of 67 are 1 and 67.
Is 67 a prime number?
Yes, 67 is a prime number since it has only two factors.
What is the highest common factor of 67 and 61?
Since both are prime numbers, the highest common factor of 67 and 61 is 1.
What is the largest factors of 67?
The largest factors of 67 is 67 itself.
What is the pime factor of 67?
The prime factor of 67 is 67 itself.