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103 LearnersLast updated on September 24, 2025
GCF of 875 and 1000
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 875 and 1000.
What is the GCF of 875 and 1000?
The greatest common factor of 875 and 1000 is 125. 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.
How to find the GCF of 875 and 1000?
To find the GCF of 875 and 1000, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 875 and 1000 by Using Listing of Factors
Steps to find the GCF of 875 and 1000 using the listing of factors:
Step 1: Firstly, list the factors of each number. Factors of 875 = 1, 5, 25, 35, 125, 175, 875. Factors of 1000 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
Step 2: Now, identify the common factors of them. Common factors of 875 and 1000: 1, 5, 25, 125.
Step 3: Choose the largest factor. The largest factor that both numbers have is 125. The GCF of 875 and 1000 is 125.
GCF of 875 and 1000 Using Prime Factorization
To find the GCF of 875 and 1000 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number. Prime Factors of 875: 875 = 5 x 5 x 5 x 7 = 53 x 7 Prime Factors of 1000: 1000 = 2 x 2 x 2 x 5 x 5 x 5 = 23 x 53
Step 2: Now, identify the common prime factors. The common prime factor is: 5 x 5 x 5 = 53
Step 3: Multiply the common prime factors. 53 = 125. The Greatest Common Factor of 875 and 1000 is 125.
GCF of 875 and 1000 Using Division Method or Euclidean Algorithm Method
Find the GCF of 875 and 1000 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number. Here, divide 1000 by 875. 1000 ÷ 875 = 1 (quotient), The remainder is calculated as 1000 − (875×1) = 125. The remainder is 125, not zero, so continue the process.
Step 2: Now divide the previous divisor (875) by the previous remainder (125). Divide 875 by 125. 875 ÷ 125 = 7 (quotient), remainder = 875 − (125×7) = 0. The remainder is zero, the divisor will become the GCF.
The GCF of 875 and 1000 is 125.
Common Mistakes and How to Avoid Them in GCF of 875 and 1000
Finding the GCF of 875 and 1000 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 875, students may mention 15, which is incorrect.
To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 875 and 1000 Examples
Problem 1
A baker has 875 grams of flour and 1000 grams of sugar. She wants to pack them into bags with the largest possible equal weight of each ingredient. What should be the weight of each bag?
We should find the GCF of 875 and 1000. GCF of 875 and 1000 5^3 = 125. There are 125 grams in each bag.
Explanation
As the GCF of 875 and 1000 is 125, the baker can make bags with 125 grams of each ingredient.
Problem 2
A farmer has 875 apples and 1000 oranges. He wants to distribute them into baskets with the same total number of fruits in each basket, using the largest possible number. How many fruits will be in each basket?
GCF of 875 and 1000 5^3 = 125. So each basket will have 125 fruits.
Explanation
There are 875 apples and 1000 oranges.
To find the total number of fruits in each basket, we should find the GCF of 875 and 1000.
There will be 125 fruits in each basket.
Problem 3
A tailor has 875 meters of red fabric and 1000 meters of blue fabric. She wants to cut both fabrics 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 875 and 1000. The GCF of 875 and 1000 5^3 = 125. The fabric pieces are 125 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 875 and 1000, which is 125.
The length of each piece of fabric will be 125 meters.
Problem 4
A carpenter has two wooden planks, one 875 cm long and the other 1000 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 875 and 1000 5^3 = 125. The longest length of each piece is 125 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 875 cm and 1000 cm, respectively.
We have to find the GCF of 875 and 1000, which is 125 cm.
The longest length of each piece is 125 cm.
Problem 5
If the GCF of 875 and ‘a’ is 125, and the LCM is 7000, find ‘a’.
The value of ‘a’ is 1000.
Explanation
GCF x LCM = product of the numbers
125 × 7000 = 875 × a
875000 = 875a
a = 875000 ÷ 875
= 1000
FAQs on the Greatest Common Factor of 875 and 1000
1.What is the LCM of 875 and 1000?
2.Is 875 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 1000?
5.Are 875 and 1000 prime numbers?
Important Glossaries for GCF of 875 and 1000
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 125 are 1, 5, 25, and 125.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 875 are 5 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 875 and 1000 is 7000.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
