Factors of 140 Using Prime Factorization
Factors of 140
The set of numbers that divide 140 evenly or into equal parts are considered to be the factors of 140. Additionally, 140 is also a composite number, which means it has more than two factors.
When you divide 140 by its factor, you get a natural number as the quotient and zero as the remainder.
For example 140 divided by 2 equals 70, with no remainder, so 2 is a factor of 140.
When a number is divided by its factor the quotient obtained is also a factor of the number. So in this case, 70 is also a factor of 140.
How to Find the Factors of the Number 140?
Factors of 140 are natural numbers that completely divide the original number without leaving a remainder. To determine the factors, we must look for numbers that can divide 140 into equal parts. As we all know, all numbers are divisible by 1, hence 1 is a factor of 140. Furthermore, because 140 is an even number and its ones place digit is 0, it is divisible by 2, 5 and 10. Let’s now look for more of these factors.
Number | Can this Number be a Factor of 20? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 140 = 140 |
2 | Yes, 140 is an even number | 2 x 70 = 140 |
3 | No, 1 + 4 + 0 = 5, 5 is not divisible by 3 | |
4 | Yes, 140 \(\div\) 4 = 35, R0 | 4 x 35 = 140 |
5 | Yes, the ones place digit of 140 is 0 | 5 x 28 = 140 |
6 | No, 140 is even but it is not divisible by 3 | |
7 | Yes, 140 \(\div\) 7 = 20, R0 | 7 x 20 = 140 |
8 | No, 140 \(\div\) 8 = 17, R4 | |
9 | No, 140 \(\div\) 9 = 15, R5 | |
10 | Yes, 140 \(\div\) 10 = 14, R0 | 10 x 14 = 140 |
11 | No, 140 \(\div\) 11 = 12, R8 | |
12 | No, 140 \(\div\) 12 = 11, R8 | |
13 | No, 140 \(\div\) 13 = 10, R10 | |
14 | Yes, ones place digit of 140 is 0 | 14 x 10 = 140 |
After this step we see that the factor pairs will start to repeat. So we can stop checking for factors at 14. The factors of 140 will be the unique multiplicands of the multiplication equations.
Hence the factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70 and 140.
Prime Factorization of 140
Prime factorization refers to expressing a number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of the original number.
The factor tree below shows the prime factorization of 140.
Therefore, prime factorization of 140 is 2 x 2 x 5 x 7, and its prime factors are 2, 5 and 7.
Factor Pairs of 140
To find the factor pairs of 140, we need to find two numbers whose product is 140.
Factors of 140 | Factor Pairs of 140 |
|---|---|
1 × 140 = 140 | (1, 140) |
2 × 70 = 140 | (2, 70) |
4 × 35 = 140 | (4, 35) |
5 x 28 = 140 | (5, 28) |
7 × 20 = 140 | (7, 20) |
10 × 14 = 140 | (10, 14) |
Therefore, the factor pairs of 140 are (1, 140), (2, 70), (4, 35) (5, 28), (7, 20) and (10, 14).
Read More:
Rapid Recall
Factors of 140:
Solved Factors of 140 Examples
Example 1: What are the common factors of 144 and 140?
Solution:
Let’s look at the factors of 140 and 144.
Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
After observing the list of factors, we can observe that the common factors of 140 and 144 are 1, 2 and 4.
Example 2: What is the greatest common factor (GCF) for the numbers 140 and 100?
Solution:
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140.
As a result, the GCF of 140 and 100 is 20.
Example 3: A team of volunteers decides to distribute health kits at two locations each having 28 and 35 families respectively. The total number of health kits needed to be distributed equally at each location is 140. How many kits will each family receive?
Solution:
140 kits are distributed equally among 28 and 35 families at two locations respectively.
So to find the number of kits received by each family we will list the factor pairs of 140:
(1, 140), (2, 70), (4, 35) (5, 28), (7, 20) and (10, 14).
Here we can see that the factors corresponding to the number of families are (5, 28) and (4, 35) .
Hence, each family at the two locations will receive 5 kits and 4 kits respectively.
The factors of the number 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. So, 140 has 12 factors.
No, the number 140 isn’t a perfect square.
140, 280, 420, 560, 700, and so on are the multiples of 140.
The number 140 has more than two factors. So 140 is not a prime number.
The greatest factor of 140 is 140.