GCF of 60 and 70
2026-02-28 18:01 Diff
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Last updated on September 19, 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 60 and 70.

What is the GCF of 60 and 70?

The greatest common factor of 60 and 70 is 10. 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 60 and 70?

To find the GCF of 60 and 70, a few methods are described below:

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 60 and 70 by Using Listing of factors

Steps to find the GCF of 60 and 70 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70.

Step 2: Now, identify the common factors of them Common factors of 60 and 70: 1, 2, 5, 10.

Step 3: Choose the largest factor The largest factor that both numbers have is 10.

The GCF of 60 and 70 is 10.

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GCF of 60 and 70 Using Prime Factorization

To find the GCF of 60 and 70 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 60: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

Prime Factors of 70: 70 = 2 × 5 × 7 = 2 × 5 × 7

Step 2: Now, identify the common prime factors The common prime factors are: 2 × 5

Step 3: Multiply the common prime factors 2 × 5 = 10.

The Greatest Common Factor of 60 and 70 is 10.

GCF of 60 and 70 Using Division Method or Euclidean Algorithm Method

Find the GCF of 60 and 70 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 70 by 60 70 ÷ 60 = 1 (quotient),

The remainder is calculated as 70 − (60×1) = 10 The remainder is 10, not zero, so continue the process

Step 2: Now divide the previous divisor (60) by the previous remainder (10)

Divide 60 by 10 60 ÷ 10 = 6 (quotient), remainder = 60 − (10×6) = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 60 and 70 is 10.

Common Mistakes and How to Avoid Them in GCF of 60 and 70

Finding the GCF of 60 and 70 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A teacher has 60 apples and 70 oranges. 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?

Okay, lets begin

We should find the GCF of 60 and 70 GCF of 60 and 70 2 × 5 = 10.

There are 10 equal groups 60 ÷ 10 = 6 70 ÷ 10 = 7

There will be 10 groups, and each group gets 6 apples and 7 oranges.

Explanation

As the GCF of 60 and 70 is 10, the teacher can make 10 groups.

Now divide 60 and 70 by 10.

Each group gets 6 apples and 7 oranges.

Well explained 👍

Problem 2

A school has 60 red flags and 70 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?

Okay, lets begin

GCF of 60 and 70 2 × 5 = 10. So each row will have 10 flags.

Explanation

There are 60 red and 70 blue flags. To find the total number of flags in each row, we should find the GCF of 60 and 70.

There will be 10 flags in each row.

Well explained 👍

Problem 3

A tailor has 60 meters of green fabric and 70 meters of yellow 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 60 and 70

The GCF of 60 and 70 2 × 5 = 10.

The fabric is 10 meters long.

Explanation

For calculating the longest length of the fabric, first, we need to calculate the GCF of 60 and 70, which is 10.

The length of each piece of the fabric will be 10 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 60 cm long and the other 70 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 60 and 70 2 × 5 = 10.

The longest length of each piece is 10 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 60 cm and 70 cm, respectively, we have to find the GCF of 60 and 70, which is 10 cm.

The longest length of each piece is 10 cm.

Well explained 👍

Problem 5

If the GCF of 60 and ‘b’ is 10, and the LCM is 420. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 70.

Explanation

GCF × LCM = product of the numbers

10 × 420 = 60 × b

4200 = 60b

b = 4200 ÷ 60 = 70

Well explained 👍

FAQs on the Greatest Common Factor of 60 and 70

1.What is the LCM of 60 and 70?

The LCM of 60 and 70 is 420.

2.Is 60 divisible by 3?

Yes, 60 is divisible by 3 because the sum of its digits (6 + 0) is divisible by 3.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 70?

The prime factorization of 70 is 2 × 5 × 7.

5.Are 60 and 70 prime numbers?

No, 60 and 70 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 60 and 70

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 9 is divided by 4, the remainder is 1 and the quotient is 2.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 60 and 70 is 420.

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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.