311 LearnersLast updated on May 26th, 2025
Factors of 154
Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 154. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 154.
Finding the Square Root of 250
We can find the square root of a number by using methods like: Prime Factorization; Long Division method; Approximation method and Subtraction method:
How to Find the Factors of 154
For finding factors of 154, we will be learning these below-mentioned methods:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors using Multiplication Methods
This particular method often finds the pair of factors which, on multiplication together, produces 154. Let us find the pairs which, on multiplication, yields 154.
1×154=154
2×77=154
7×22=154
11×14=154
So, factors of 154 are: 1,2,7,11,14,22,77, and 154.
Finding Factors using Division Method
The division method finds the factors that evenly divides the given number 154. In this process, we have to divide 154 by all possible natural numbers less than 154 and check.
1,2,7,11,14,22,77, and 154 are the only factors that the number 154 has. So to verify the factors of 154 using the division method, we just need to divide 154 by each factor.
154/1 =154
154/2=77
154/7=22
154/11=14
154/14=11
154/22=7
154/77=2
154/154=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 154 into a product of its prime integers.
Prime Factors of 154: 2,7,11.
Prime Factorization of 154: 2×7×11
Factor tree:
The number 154 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 154.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 154 are 2 and 77, then proceeding to 77, we get 7 and 11. So, now the factor tree for 154 is achieved.
Factor Pairs
Positive pair factors: (1,154), (2,77), (7,22), (11,14).
Negative pair factors: (-1,-154), (-2,-77), (-7,-22), (-11,-14).
Common Mistakes and How to Avoid Them in Factors of 154
Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them.
Mistake 1
Factors might be larger than the given number.
Factors can never be larger than the given number, but multiples can be. You need to understand the concept that factors are integers which divide a given number perfectly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 154 Examples
Problem 1
Find the GCF of 154 and 160
Factors of 154: 1,2,7,11,14,22,77,154
Factors of 160: 1,2,4,5,8,10,16,20,32,40,80,60
Common factors of 154 and 160: 1,2
So, the Greatest Common Factor of 154 and 160 is 2.
Answer: 2
Explanation
We first listed out the factors of 154 and 160 and then found the common factors and then identified the greatest common factor from the common list.
Problem 2
Find the LCM of 154 and 77
Prime factorization of 77: 7×11.
Prime factorization of 154: 2×7×11
LCM of 77 and 154: 2×7×11= 154.
Answer: 154
Explanation
Did prime factorization of both 77 and 154. The LCM is the product of the highest power of each factor.
Problem 3
The area of a rectangle is 154 square units. If the length is 77 units, then what is the measure of its width?
Area of rectangle: 154 sq units
Factors of 154: 1,2,7,11,14,22,77,154
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 77 units
There exists a factor pair of 154, which is (2,77). Hence, width is 2 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 77 × width = 154
⇒ width = 154/77 = 2
Answer: 2 units
Explanation
Used the concept of factor pairs for 154 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 2,7,11,77.
Prime factorization of 2: 2×1.
Prime factorization of 7: 7×1
Prime factorization of 11: 11×1
Prime factorization of 77: 11×7
LCM of 2,7,11,77: 2×11×7 = 154
Answer: 154 is the smallest number which is divisible by 2,7,11,77.
Explanation
To find the smallest number which is divisible by 2,7,11,77, we need to find the LCM of these numbers.
Problem 5
What is the sum of the factors of 77 and 154?
Factors of 54: 1,2,7,11,14,22,77,154
Sum of the factors: 1+2+7+11+14+22+77+154= 288
Factors of 77: 1,7,11,77
Explanation
Sum of the factors: 1+7+11+77 =96
FAQs on Factors of 154
1.How to make 154 in multiplication?
2.What are all 155 factors?
3.List down all the 159 factors?
4.Is prime factorization possible for 154?
5.What are 153 factors?
6.How can children in Philippines use numbers in everyday life to understand Factors of 154?
7.What are some fun ways kids in Philippines can practice Factors of 154 with numbers?
8.What role do numbers and Factors of 154 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 154 skills?
Important Glossaries for Factors of 154
- Multipliers - Number which multiplies or a number by which another number is multiplied.
- Dividers - A number that divides.
- Prime Factorization - It involves factoring the number into its prime factors.
- Prime factors - These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.
- Composite numbers - These are numbers having more than two factors.
- Multiple - It is a product of the given number and any other integer.
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About BrightChamps in Philippines
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
