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107 LearnersLast updated on September 24, 2025
GCF of 625 and 1000
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 625 and 1000.
What is the GCF of 625 and 1000?
The greatest common factor of 625 and 1000 is 125. 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.
How to find the GCF of 625 and 1000?
To find the GCF of 625 and 1000, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 625 and 1000 by Using Listing of Factors
Steps to find the GCF of 625 and 1000 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 625 = 1, 5, 25, 125, 625.
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 625 and 1000: 1, 5, 25, 125.
Step 3: Choose the largest factor The largest factor that both numbers have is 125.
The GCF of 625 and 1000 is 125.
GCF of 625 and 1000 Using Prime Factorization
To find the GCF of 625 and 1000 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 625: 625 = 5 × 5 × 5 × 5 = 54
Prime Factors of 1000: 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53
Step 2: Now, identify the common prime factors The common prime factors are: 5 × 5 × 5 = 53
Step 3: Multiply the common prime factors 53 = 125.
The Greatest Common Factor of 625 and 1000 is 125.
GCF of 625 and 1000 Using Division Method or Euclidean Algorithm Method
Find the GCF of 625 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 625 1000 ÷ 625 = 1 (quotient),
The remainder is calculated as 1000 − (625×1) = 375
The remainder is 375, not zero, so continue the process
Step 2: Now divide the previous divisor (625) by the previous remainder (375)
Divide 625 by 375 625 ÷ 375 = 1 (quotient), remainder = 625 − (375×1) = 250
The remainder is 250, not zero, so continue the process
Step 3: Now divide the previous divisor (375) by the previous remainder (250)
Divide 375 by 250 375 ÷ 250 = 1 (quotient), remainder = 375 − (250×1) = 125
The remainder is 125, not zero, so continue the process
Step 4: Now divide the previous divisor (250) by the previous remainder (125)
Divide 250 by 125 250 ÷ 125 = 2 (quotient), remainder = 250 − (125×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 625 and 1000 is 125.
Common Mistakes and How to Avoid Them in GCF of 625 and 1000
Finding GCF of 625 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 625, students may mention 10 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 with 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 that 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 625 and 1000 Examples
Problem 1
A teacher has 625 pencils and 1000 erasers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 625 and 1000 GCF of 625 and 1000 53 = 125.
There are 125 equal groups 625 ÷ 125 = 5 1000 ÷ 125 = 8
There will be 125 groups, and each group gets 5 pencils and 8 erasers.
Explanation
As the GCF of 625 and 1000 is 125, the teacher can make 125 groups.
Now divide 625 and 1000 by 125.
Each group gets 5 pencils and 8 erasers.
Problem 2
A school has 625 red chairs and 1000 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 625 and 1000 53 = 125.
So each row will have 125 chairs.
Explanation
There are 625 red and 1000 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 625 and 1000.
There will be 125 chairs in each row.
Problem 3
A tailor has 625 meters of red ribbon and 1000 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 625 and 1000
The GCF of 625 and 1000 53 = 125.
The ribbon is 125 meters long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 625 and 1000 which is 125.
The length of each piece of the ribbon will be 125 meters.
Problem 4
A carpenter has two wooden planks, one 625 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 625 and 1000 53 = 125.
The longest length of each piece is 125 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 625 cm and 1000 cm, respectively.
We have to find the GCF of 625 and 1000, which is 125 cm.
The longest length of each piece is 125 cm.
Problem 5
If the GCF of 625 and ‘a’ is 125, and the LCM is 5000. Find ‘a’.
The value of ‘a’ is 1000.
Explanation
GCF × LCM = product of the numbers
125 × 5000 = 625 × a
625000 = 625a
a = 625000 ÷ 625 = 1000
FAQs on the Greatest Common Factor of 625 and 1000
1.What is the LCM of 625 and 1000?
2.Is 625 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 1000?
5.Are 625 and 1000 prime numbers?
Important Glossaries for GCF of 625 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, 25, 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 1000 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 1000 is divided by 625, the remainder is 375 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 625 and 1000 is 5000.
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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.
