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103 LearnersLast updated on September 24, 2025
GCF of 84 and 630
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 84 and 630.
What is the GCF of 84 and 630?
The greatest common factor of 84 and 630 is 42. 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 84 and 630?
To find the GCF of 84 and 630, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 84 and 630 by Using Listing of Factors
Steps to find the GCF of 84 and 630 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Factors of 630 = 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630.
Step 2: Now, identify the common factors of them Common factors of 84 and 630: 1, 2, 3, 6, 7, 14, 21, 42.
Step 3: Choose the largest factor The largest factor that both numbers have is 42. The GCF of 84 and 630 is 42.
GCF of 84 and 630 Using Prime Factorization
To find the GCF of 84 and 630 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3 x 7 Prime Factors of 630: 630 = 2 x 3 x 3 x 5 x 7 = 2 x 3² x 5 x 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 3 x 7
Step 3: Multiply the common prime factors 2 x 3 x 7 = 42. The Greatest Common Factor of 84 and 630 is 42.
GCF of 84 and 630 Using Division Method or Euclidean Algorithm Method
Find the GCF of 84 and 630 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 630 by 84 630 ÷ 84 = 7 (quotient), The remainder is calculated as 630 − (84×7) = 42 The remainder is 42, not zero, so continue the process
Step 2: Now divide the previous divisor (84) by the previous remainder (42) Divide 84 by 42 84 ÷ 42 = 2 (quotient), remainder = 84 − (42×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 84 and 630 is 42.
Common Mistakes and How to Avoid Them in GCF of 84 and 630
Finding the GCF of 84 and 630 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 84, 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 indicates an 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 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 84 and 630 Examples
Problem 1
A chef has 84 lemons and 630 oranges. She wants to group them into equal sets, with the largest number of fruits in each group. How many fruits will be in each group?
We should find the GCF of 84 and 630 GCF of 84 and 630 2 x 3 x 7 = 42. There are 42 equal groups 84 ÷ 42 = 2 630 ÷ 42 = 15 There will be 42 groups, and each group gets 2 lemons and 15 oranges.
Explanation
As the GCF of 84 and 630 is 42, the chef can make 42 groups.
Now divide 84 and 630 by 42.
Each group gets 2 lemons and 15 oranges.
Problem 2
A school has 84 red markers and 630 blue markers. They want to arrange them in rows with the same number of markers in each row, using the largest possible number of markers per row. How many markers will be in each row?
GCF of 84 and 630 2 x 3 x 7 = 42. So each row will have 42 markers.
Explanation
There are 84 red and 630 blue markers.
To find the total number of markers in each row, we should find the GCF of 84 and 630.
There will be 42 markers in each row.
Problem 3
A tailor has 84 meters of red fabric and 630 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 84 and 630 The GCF of 84 and 630 2 x 3 x 7 = 42. The fabric is 42 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 84 and 630, which is 42.
The length of each piece of fabric will be 42 meters.
Problem 4
A carpenter has two wooden planks, one 84 cm long and the other 630 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 84 and 630 2 x 3 x 7 = 42. The longest length of each piece is 42 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 84 cm and 630 cm, respectively, we have to find the GCF of 84 and 630, which is 42 cm.
The longest length of each piece is 42 cm.
Problem 5
If the GCF of 84 and ‘b’ is 42, and the LCM is 1260. Find ‘b’.
The value of ‘b’ is 210.
Explanation
GCF x LCM = product of the numbers
42 × 1260 = 84 × b
52920 = 84b
b = 52920 ÷ 84
= 210
FAQs on the Greatest Common Factor of 84 and 630
1.What is the LCM of 84 and 630?
2.Is 84 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 630?
5.Are 84 and 630 prime numbers?
Important Glossaries for GCF of 84 and 630
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, 30, 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 30 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 84 and 630 is 1260.
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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.
