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 28 and 70.
The greatest common factor of 28 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 28 and 70, a few methods are described below:
Steps to find the GCF of 28 and 70 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 28 = 1, 2, 4, 7, 14, 28.
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70.
Step 2: Now, identify the common factors of them.
Common factors of 28 and 70: 1, 2, 7, 14.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 14.
The GCF of 28 and 70 is 14.
To find the GCF of 28 and 70 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime factors of 28: 28 = 2 x 2 x 7 = 22 x 7
Prime factors of 70: 70 = 2 x 5 x 7 = 2 x 5 x 7
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 x 7 = 21 x 7
Step 3: Multiply the common prime factors 2 x 7 = 14.
The Greatest Common Factor of 28 and 70 is 14.
Find the GCF of 28 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 28 70 ÷ 28 = 2 (quotient), The remainder is calculated as 70 − (28 x 2) = 14
The remainder is 14, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (14)
Divide 28 by 14 28 ÷ 14 = 2 (quotient), remainder = 28 − (14 x 2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 28 and 70 is 14.
Finding GCF of 28 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 28 roses and 70 tulips. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 28 and 70 GCF of 28 and 70
2 x 7 = 14.
There are 14 equal bouquets
28 ÷ 14 = 2
70 ÷ 14 = 5
There will be 14 bouquets, and each bouquet gets 2 roses and 5 tulips.
As the GCF of 28 and 70 is 14, the gardener can make 14 bouquets.
Now divide 28 and 70 by 14.
Each bouquet gets 2 roses and 5 tulips.
A chef has 28 apples and 70 oranges. She wants to make fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 28 and 70
2 x 7 = 14.
So each basket will have 14 fruits.
There are 28 apples and 70 oranges.
To find the total number of fruits in each basket, we should find the GCF of 28 and 70.
There will be 14 fruits in each basket.
A tailor has 28 meters of green ribbon and 70 meters of yellow 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 28 and 70
The GCF of 28 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 28 and 70, which is 14. The length of each piece of the ribbon will be 14 meters.
A carpenter has two wooden planks, one 28 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 28 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, 28 cm and 70 cm, respectively, we have to find the GCF of 28 and 70, which is 14 cm.
The longest length of each piece is 14 cm.
If the GCF of 28 and 'b' is 14, and the LCM is 140. Find 'b'.
The value of 'b' is 70.
GCF x LCM = product of the numbers
14 x 140 = 28 x b
1960 = 28b
b = 1960 ÷ 28 = 70
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.