Factors of 154
Factors of 154 are the list of integers that we can split evenly into 154. There are overall 8 factors of 154 i.e. 1, 2, 7, 11, 14, 22, 77, 154 where 154 is the biggest factor. The Pair Factors of 154 are (1, 154), (2, 77), (7, 22), (11, 14) and its Prime Factors are 2 × 7 × 11.
- All Factors of 154: 1, 2, 7, 11, 14, 22, 77 and 154
- Negative Factors of 154: -1, -2, -7, -11, -14, -22, -77 and -154
- Prime Factors of 154: 2, 7, 11
- Prime Factorization of 154: 21 × 71 × 111
- Sum of Factors of 154: 288
1. | What Are the Factors of 154? |
2. | Factors of 154 by Prime Factorization |
3. | Factors of 154 in Pairs |
4. | FAQs on Factors of 154 |
What are Factors of 154?
Factors of 154 are pairs of those numbers whose products result in 154. These factors are either prime numbers or composite numbers.
How to Find the Factors of 154?
To find the factors of 154, we will have to find the list of numbers that would divide 154 without leaving any remainder.
- 154/11 = 14; therefore, 11 is a factor of 154 and 14 is also a factor of 154.
- 154/77 = 2; therefore, 77 is a factor of 154 and 2 is also a factor of 154.
☛ Also Check:
- Factors of 121 - The factors of 121 are 1, 11, 121
- Factors of 78 - The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
- Factors of 39 - The factors of 39 are 1, 3, 13, 39
- Factors of 27 - The factors of 27 are 1, 3, 9, 27
- Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 154 by Prime Factorization
- 154 ÷ 2 = 77
Further dividing 77 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 77 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 154 can be written as 21 × 71 × 111 where 2, 7, 11 are prime.
Factors of 154 in Pairs
Pair factors of 154 are the pairs of numbers that when multiplied give the product 154. The factors of 154 in pairs are:
- 1 × 154 = (1, 154)
- 2 × 77 = (2, 77)
- 7 × 22 = (7, 22)
- 11 × 14 = (11, 14)
Negative pair factors of 154 are:
- -1 × -154 = (-1, -154)
- -2 × -77 = (-2, -77)
- -7 × -22 = (-7, -22)
- -11 × -14 = (-11, -14)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 154 Solved Examples
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Example 1: How many factors are there for 154?
Solution:
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154. Therefore, 154 has 8 factors.
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Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 154 and 59.
Solution:
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154 and factors of 59 are 1, 59.
Therefore, the Lowest Common Multiple (LCM) of 154 and 59 is 9086 and Greatest Common Factor (GCF) of 154 and 59 is 1. -
Example 3: Find if 2, 11, 14, 22 and 119 are factors of 154.
Solution:
When we divide 154 by 119 it leaves a remainder. Therefore, the number 119 is not a factor of 154. All numbers except 119 are factors of 154.
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Example 4: Find the product of all the prime factors of 154.
Solution:
Since, the prime factors of 154 are 2, 7, 11. Therefore, the product of prime factors = 2 × 7 × 11 = 154.
FAQs on Factors of 154
What are the Factors of 154?
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154 and its negative factors are -1, -2, -7, -11, -14, -22, -77, -154.
What is the Sum of all the Factors of 154?
Sum of all factors of 154 = (21 + 1 - 1)/(2 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 288
What are the Prime Factors of 154?
The prime factors of 154 are 2, 7, 11.
What is the Greatest Common Factor of 154 and 55?
The factors of 154 and 55 are 1, 2, 7, 11, 14, 22, 77, 154 and 1, 5, 11, 55 respectively.
Common factors of 154 and 55 are [1, 11].
Hence, the GCF of 154 and 55 is 11.
How Many Factors of 154 are also common to the Factors of 111?
Since, the factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154 and factors of 111 are 1, 3, 37, 111. Hence, 154 and 111 have only one common factor which is 1. Therefore, 154 and 111 are co-prime.
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