Definition of factors of 77: If a number completely divides 77 without leaving a remainder, then that number is called a factor of 77. Thus, we can say that the factors of 77 are the divisors of 77.
Here, we will learn about the factors of 77 and the prime factors of 77. We have:
- 77 = 7×11 is the prime factorization of 77.
- The factors of 77 are 1, 7, 11, and 77.
- The prime factors of 77 are 7 and 11.
- Negative factors of 77 are –1, -7, -11, and –77.
Table of Contents
What are the Factors of 77?
Let us write the number 77 multiplicatively in all possible ways. We definitely have:
| 77 = 1×77 |
| 77 = 7×11 |
As there are no other ways we can write 77 multiplicatively, so we will stop right now. So the factors of 77 in pairs are given as follows:
| 77 = a×b | Factors in Pairs (a,b) |
| 77 = 1×77 | (1, 77) |
| 77 = 7×11 | (7, 11) |
Thus the pair factors of 77 are (1, 77) and (7, 11). As all the numbers appearing in pair factors are the factors of 77, we conclude that
|
The factors of 77 are: 1, 7, 11, and 77. |
Number of Factors of 77
From above we have calculated the factors of 77 which are 1, 7, 11, and 77.
Thus the total number of factors of 77 is four.
Prime Factors of 77
Note that the factors of 77 are 1, 7, 11, and 77. Among those factors, we observe that only 7 and 11 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 77 are 7 and 11.
Question: What are the factors of 77?
Video Solution:
How to Find Factors of 77?
Now we will determine the factors of 77 by division method. In this method, we will try to find the numbers that can divide 77 with no remainder. See that
77/1=77 and the remainder is 0.
∴ 1 and 77 are factors of 77.
77/7=11 and the remainder is 0.
∴ 7 and 11 are factors of 77.
Note that no numbers other than the numbers in violet color can divide 77. So the numbers in violet color, that is, 1, 7, 11, and 77 are the complete list of factors of 77.
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