Last updated on May 26th, 2025
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.
We can find the square root of a number by using methods like: Prime Factorization; Long Division method; Approximation method and Subtraction method:
For finding factors of 154, we will be learning these below-mentioned 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.
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 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
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.
Positive pair factors: (1,154), (2,77), (7,22), (11,14).
Negative pair factors: (-1,-154), (-2,-77), (-7,-22), (-11,-14).
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.
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
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.
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
Did prime factorization of both 77 and 154. The LCM is the product of the highest power of each factor.
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
Used the concept of factor pairs for 154 and rechecked using the formula for finding area of a rectangle.
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.
To find the smallest number which is divisible by 2,7,11,77, we need to find the LCM of these numbers.
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
Sum of the factors: 1+7+11+77 =96
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.
: She loves to read number jokes and games.