Factors
Factors of 71 | Prime Factorization of 71 | Factor Tree of 71
Written by Prerit Jain
Updated on: 24 Aug 2023
Contents
Factors of 71 | Prime Factorization of 71 | Factor Tree of 71
Factors of 71
| Factors of 71 | Factor Pairs of 71 | Prime factors of 71 |
| 1, 71 | (1,71) | 1 x 71 |
Calculate Factors of
The Factors are
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What are the factors of 71
To find the factors of a number, you can divide it by other numbers to see if there is no remainder. This means you can check which numbers can be evenly divided into the number you are interested in. The numbers that divide evenly are called the factors of the original number.
For example, you can find the factors of 71 by dividing them by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc., and seeing which numbers result in no remainder. The factors of 71 are 1 and 71.
Another way to find the factors of a number is to use its prime factorization. Prime factorization is a list of prime numbers that can be multiplied together to give the original number. For example, the prime factorization of 71 is 1 x 71. This means that 1 and 71 are both prime numbers and when they are multiplied together, they equal 71.
Since the prime factorization of 71 is 1 x 71, the factors of 71 are 1 and 71.
How to Find Factors of 71
To find the factors of a number, you can divide it by other numbers to see if there is no remainder. This means you can check which numbers can be evenly divided into the number you are interested in. The numbers that divide evenly are called the factors of the original number.
For example, you can find the factors of 71 by dividing them by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc., and seeing which numbers result in no remainder. The factors of 71 are 1 and 71.
Another way to find the factors of a number is to use its prime factorization. Prime factorization is a list of prime numbers that can be multiplied together to give the original number. For example, the prime factorization of 71 is 1 x 71. This means that 1 and 71 are both prime numbers and when they are multiplied together, they equal 71.
Since the prime factorization of 71 is 1 x 71, the factors of 71 are 1 and 71. These are all the numbers that can be obtained by multiplying together some combination of 1 and 71.
Factors of 71 Using the Multiplication Method
To find the factors of a number using the multiplication method, you can list out all the pairs of numbers that can be multiplied together to give the original number. For example, to find the factors of 71, you can list out all the pairs of numbers that can be multiplied together to give 71.
Some examples of pairs of factors of 71 include (1, 71). To find all the factors of 71, you can continue listing out all the pairs of numbers that can be multiplied together to give 71.
Some other pairs of factors of 71 include (1, 71) and (71, 1).
Factors of 71 Using the Division Method
To find the factors of a number using the division method, you can divide the number by each number from 1 to the number itself, and check which numbers result in no remainder. The numbers that divide evenly into the original number are called factors.
For example, to find the factors of 71 using the division method, you can divide 71 by each number from 1 to 71 and see which numbers divide evenly into 71. Some examples of this process include:
- Divide 71 by 1. 71 ÷ 1 = 71, with no remainder. 1 is a factor of 71.
- Divide 71 by 2. 71 ÷ 2 = 35.5, with a remainder of 0.5. 2 is not a factor of 71.
- Divide 71 by 3. 71 ÷ 3 = 23.66, with a remainder of 0.66. 3 is not a factor of 71.
- Divide 71 by 4. 71 ÷ 4 = 17.75, with a remainder of 0.75. 4 is not a factor of 71.
By continuing this process, you can find all the factors of 71. The factors of 71 are 1 and 71.
Prime Factorization of 71
Calculate Prime Factors of
The Prime Factors of 71 =
71
The prime factorization of 71 is the expression of 71 as the product of its prime factors. Because 71 is a prime number, its prime factorization is simply 71 itself. This means that the prime factorization of 71 is written as 71.
To find the prime factorization of a number, you can express the number as the product of its prime factors. For example, the prime factorization of 15 is 3 x 5, because 15 can be expressed as the product of the prime numbers 3 and 5 (3 x 5 = 15).
The prime factorization of a number is written as the product of its prime factors. For example, the prime factorization of 71 is written as 71.
Factor tree of 71
A factor tree is a graphical representation of the prime factorization of a number. To find the factor tree of 71, you can follow these steps:
- Write the number 71 on a piece of paper.
- Find the smallest prime factor of 71. The smallest prime factor of 71 is 1.
- Divide 71 by 1 and write the result, 71, on the branch below 71.
Your factor tree should now look like this:71
/
1 71
71
To show that the factor tree is complete, you can draw a circle around the prime numbers, like this:
71
/
1 71
(71)
This shows that the prime factorization of 71 is 1 x 71 and that 1 and 71 are the prime factors of 71.
Factor Pairs of 71
Calculate Pair Factors of
1 x 71=71
So Pair Factors of 71 are
(1,71)
A factor pair of a number is a pair of numbers that can be multiplied together to give the original number. For example, the factor pairs of 71 include (1, 71).
To find all the factor pairs of 71, you can list out all the pairs of numbers that can be multiplied together to give 71. Some other pairs of factors include (1, 71) and (71, 1).
It is important to note that the order of the numbers in a factor pair does not matter. For example, (1, 71) and (71, 1) are both factor pairs of 71, because 1 x 71 = 71 and 71 x 1 = 71.
More Factors
- Factors of 68
- Factors of 69
- Factors of 70
- Factors of 71
- Factors of 72
- Factors of 73
- Factors of 74
Factors of 71 – Quick Recap
Factors of 71: 1 and 71
Negative Factors of 71: (-1, -71)
Prime Factors of 71: 1 x 71
Prime Factorization of 71: 71
Factors of 71 – Fun Facts
- The factors of 71 are all the numbers that can be evenly divided into 71.
- The prime factors of 71 are 1 and 71 because they are the prime numbers that can be multiplied together to give 71 (1 x 71 = 71).
- The factors of 71 include 1 and 71.
- 71 is a prime number, which means that it has only two factors: 1 and itself.
- The sum of the factors of 71 (1 + 71) is 72.
Also Check: Multiples, Square Root, and LCM
Solved Examples of Factor 71
Q.1: What pairs of numbers multiplied together would equal seventy-one? Answer: Two numbers which when multiplied together would equal seventy-one are 1×71.
Q.2: If you divide seventy-one by three, what will the remainder be?
Answer: The remainder when dividing seventy-one by three is two; 71/3= 23 with a remainder of 2.
Q.3: How many even numbers remain between one and seventy-one when all odd numbers are removed?
Answer: Thirty-six even numbers remain between one and seventy-one when all odd numbers are removed; these would include 2, 4, 6, 8 10, 12 14, 16 18, 20 22, 24 26, 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 & 70.
Q.4: Find the prime factorization of seventy-one.
Answer: The prime factorization of seventy-one is 71 = 1 x 71; both being prime numbers.
Q.5: Is seventy-one a prime factor of twelve hundred and twelve?
Answer: No, seventy-one is not a prime factor of twelve hundred and twelve; As on dividing 1212 by 7, the remainder is not 0.
Q.6: Find the least common multiple for forty-two and seventy-one.
Answer: The least common multiple for forty-two and seventy-one is 2982; this can be determined by multiplying both numbers together (42 x71 = 2982).
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Frequently Asked Questions on Factors of 71
Is seventy-one a prime number?
Yes, seventy-one is a prime number.
Is seventy-one divisible by nine?
No, seventy-one is not divisible by nine; 71/9 = 7.8 with 0.8 remainders.
How many factors does the number seventy-one have?
Seventy-one has two factors; these would include 1, & 71.
What is the greatest common factor of fourteen and seventy-one?
The factors of 14 are 1, 2, 7, and 14. The factors of 71 are 1 and 71.
The common factors of 14 and 71 are 1 because it is the only factor they both share.
Therefore, the greatest common factor of 14 and 71 is 1.
How many odd numbers remain between one and seventy-one when all even numbers are removed?
Thirty-five odd numbers remain between one and seventy-one when all even numbers are removed; these would include 1, 3, 5, 7, 9, 11, 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 & 69.
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