Last updated on August 5th, 2025
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 14 and 70.
The greatest common factor of 14 and 70 is 14. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
To find the GCF of 14 and 70, a few methods are described below:
Steps to find the GCF of 14 and 70 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 14 = 1, 2, 7, 14.
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70.
Step 2: Now, identify the common factors of them
Common factors of 14 and 70: 1, 2, 7, 14.
Step 3: Choose the largest factor
The largest factor that both numbers have is 14.
The GCF of 14 and 70 is 14.
To find the GCF of 14 and 70 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 14: 14 = 2 x 7
Prime Factors of 70: 70 = 2 x 5 x 7
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 7
Step 3: Multiply the common prime factors
2 x 7 = 14.
The Greatest Common Factor of 14 and 70 is 14.
Find the GCF of 14 and 70 using the Division Method or Euclidean Algorithm Method
Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 70 by 14
70 ÷ 14 = 5 (quotient)
The remainder is calculated as 70 − (14×5) = 0
Since the remainder is zero, the divisor becomes the GCF.
The GCF of 14 and 70 is 14.
Finding GCF of 14 and 70 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A gardener has 14 rose plants and 70 tulip plants. She wants to group them into equal sets with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 14 and 70
GCF of 14 and 70
2 x 7 = 14.
There are 14 equal groups
14 ÷ 14 = 1
70 ÷ 14 = 5
There will be 14 groups, and each group gets 1 rose plant and 5 tulip plants.
As the GCF of 14 and 70 is 14, the gardener can make 14 groups.
Now divide 14 and 70 by 14.
Each group gets 1 rose plant and 5 tulip plants.
A school has 14 red chairs and 70 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 14 and 70
2 x 7 = 14.
So each row will have 14 chairs.
There are 14 red and 70 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 14 and 70.
There will be 14 chairs in each row.
A tailor has 14 meters of red ribbon and 70 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 14 and 70
The GCF of 14 and 70
2 x 7 = 14.
The ribbon is 14 meters long.
For calculating the longest length of the ribbon first we need to calculate the GCF of 14 and 70 which is 14.
The length of each piece of the ribbon will be 14 meters.
A carpenter has two wooden planks, one 14 cm long and the other 70 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood
GCF of 14 and 70
2 x 7 = 14.
The longest length of each piece is 14 cm.
To find the longest length of each piece of the two wooden planks, 14 cm and 70 cm, respectively.
We have to find the GCF of 14 and 70, which is 14 cm.
The longest length of each piece is 14 cm.
If the GCF of 14 and ‘a’ is 14, and the LCM is 140. Find ‘a’.
The value of ‘a’ is 70.
GCF x LCM = product of the numbers
14 x 140 = 14 x a
1960 = 14a
a = 1960 ÷ 14 = 140
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.