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 16 and 49.
The greatest common factor of 16 and 49 is 1. The largest divisor of two or more numbers is called the GCF of the numbers. 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 16 and 49, a few methods are described below:
Steps to find the GCF of 16 and 49 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 49 = 1, 7, 49.
Step 2: Now, identify the common factors of them.
Common factor of 16 and 49: 1.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 1.
The GCF of 16 and 49 is 1.
To find the GCF of 16 and 49 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24
Prime Factors of 49: 49 = 7 x 7 = 72
Step 2: Now, identify the common prime factors. There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 16 and 49 is 1.
Find the GCF of 16 and 49 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 49 by 16 49 ÷ 16 = 3 (quotient), The remainder is calculated as 49 − (16×3) = 1
The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (16) by the previous remainder (1)
Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 16 and 49 is 1.
Finding GCF of 16 and 49 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 16 rose bushes and 49 tulip bulbs. She wants to plant them in rows with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 16 and 49 GCF of 16 and 49 is 1. There will be 1 plant in each row.
As the GCF of 16 and 49 is 1, the gardener can only plant 1 plant in each row.
A chef has 16 apples and 49 oranges. He wants to arrange them in baskets with an equal 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 16 and 49 is 1. So each basket will have 1 fruit.
There are 16 apples and 49 oranges.
To find the total number of fruits in each basket, we should find the GCF of 16 and 49.
There will be 1 fruit in each basket.
A worker has 16 meters of fabric and 49 meters of lace. She wants to cut both materials 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 16 and 49
The GCF of 16 and 49 is 1.
The length of each piece is 1 meter.
For calculating the longest length of the materials, first we need to calculate the GCF of 16 and 49, which is 1. The length of each piece of material will be 1 meter.
A carpenter has two wooden planks, one 16 cm long and the other 49 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 16 and 49 is 1.
The longest length of each piece is 1 cm.
To find the longest length of each piece of the two wooden planks, 16 cm and 49 cm, respectively.
We have to find the GCF of 16 and 49, which is 1 cm.
The longest length of each piece is 1 cm.
If the GCF of 16 and ‘b’ is 1, and the LCM is 784, find ‘b’.
The value of ‘b’ is 49.
GCF x LCM = product of the numbers
1 × 784 = 16 × b
784 = 16b
b = 784 ÷ 16 = 49
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.