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 32 and 15.
The greatest common factor of 32 and 15 is 1. 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 32 and 15, a few methods are described below -
Steps to find the GCF of 32 and 15 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 32 = 1, 2, 4, 8, 16, 32.
Factors of 15 = 1, 3, 5, 15.
Step 2: Now, identify the common factors of them Common factors of 32 and 15: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 32 and 15 is 1.
To find the GCF of 32 and 15 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 32: 32 = 2×2×2×2×2 = 2^5
Prime Factors of 15: 15 = 3×5
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: Multiply the common prime factors
Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 32 and 15 is 1.
Find the GCF of 32 and 15 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 32 by 15 32 ÷ 15 = 2 (quotient),
The remainder is calculated as 32 − (15×2) = 2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (2)
Divide 15 by 2 15 ÷ 2 = 7 (quotient), remainder = 15 − (2×7) = 1
Step 3: Now divide the previous divisor (2) by the previous remainder (1)
Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 32 and 15 is 1.
Finding GCF of 32 and 15 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A baker has 32 cupcakes and 15 cookies. She wants to arrange them into trays with the largest possible number of items in each tray, with an equal number of cupcakes and cookies in each tray. How many items will be in each tray?
We should find the GCF of 32 and 15 GCF of 32 and 15 is 1.
There will be 1 item in each tray with equal cupcakes and cookies.
As the GCF of 32 and 15 is 1, the baker can arrange 1 cupcake and 1 cookie on each tray.
A florist has 32 roses and 15 tulips. She wants to make bouquets with the same number of flowers in each bouquet, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
GCF of 32 and 15 is 1.
So each bouquet will have 1 flower of each type.
There are 32 roses and 15 tulips. To find the total number of flowers in each bouquet, we should find the GCF of 32 and 15. There will be 1 flower of each type in each bouquet.
A librarian has 32 fiction books and 15 non-fiction books. She wants to arrange them on shelves with equal books on each shelf, using the longest possible length. What should be the length of each arrangement?
For calculating the longest equal arrangement, we have to calculate the GCF of 32 and 15
The GCF of 32 and 15 is 1.
Each arrangement will have 1 book of each type.
For calculating the longest arrangement of books first, we need to calculate the GCF of 32 and 15, which is 1. Each arrangement will have 1 book of each type.
A gardener has two plots, one with 32 square meters and the other with 15 square meters. He wants to divide them into the longest possible equal sections, without any area left over. What should be the area of each section?
The gardener needs the longest section GCF of 32 and 15 is 1.
The longest area of each section is 1 square meter.
To find the longest area of each section of the two plots, 32 square meters and 15 square meters, respectively. We have to find the GCF of 32 and 15, which is 1 square meter. The longest area of each section is 1 square meter.
If the GCF of 32 and ‘b’ is 1, and the LCM is 480, find ‘b’.
The value of ‘b’ is 15.
GCF x LCM = product of the numbers 1 × 480 = 32 × b
480 = 32b
b = 480 ÷ 32 = 15
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.