GCF of 35 and 50 – How to find in Different Ways

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Created by: Team Maths - Examples.com, Last Updated: August 19, 2024

GCF of 35 and 50 – How to find in Different Ways

GCF of 35 and 50

The Greatest Common Factor (GCF) of 35 and 50 is 5. This is determined by identifying the common prime factors of the two numbers. The prime factorization of 35 is 5 × 7, and the prime factorization of 50 is 2 × 5 × 5. The only common prime factor is 5, making it the GCF of 35 and 50.

GCF of 35 and 50

GCF of 35 and 50 is 5.

Methods to Find GCF of 35 and 50

  1. Prime Factorization Method
  2. Long Division Method
  3. Listing Common Factors

GCF of 35 and 50 by Prime Factorization Method

GCF-of-35-and-50-by-Prime-Factorization-Method-1

Prime Factorization of 35:

  • 35 = 5 × 7

Prime Factorization of 50:

  • 50 = 2 × 5 × 5 (or 2×5²)

Identify Common Factors:

  • The common prime factor between 35 and 50 is 5.

Determine the GCF:

Since the only common prime factor is 5, the GCF of 35 and 50 is 5.

GCF of 35 and 50 by Long Division Method.

GCF-of-35-and-50-by-Long-Division-Method

Divide the larger number (50) by the smaller number (35):

50 ÷ 35 gives a quotient of 1 and a remainder of 15.

Replace the larger number with the smaller number (35) and the smaller number with the remainder (15):

Now, divide 35 by 15.

35 ÷ 15 gives a quotient of 2 and a remainder of 5.

Repeat the process: Replace 35 with 15 and 15 with the remainder 5.

Now, divide 15 by 5.

15 ÷ 5 gives a quotient of 3 and a remainder of 0.

When the remainder is 0, the divisors at this step is the GCF.

So, the GCF of 35 and 50 is 5.

GCF of 35 and 50 by Listing Common Factors

GCF-of-35-and-50-by-Listing-Common-Factors

List the factors of 35:

Factors of 35: 1, 5, 7, 35

List the factors of 50:

Factors of 50: 1, 2, 5, 10, 25, 50

Identify the common factors:

Common factors of 35 and 50: 1, 5

Determine the greatest common factor:

The greatest common factor is 5.

Therefore, the GCF of 35 and 50 is 5.

What is the GCF of 35 and 50?

The GCF (Greatest Common Factor) of 35 and 50 is 5.

Why is the GCF of 35 and 50 important?

The GCF is important in simplifying fractions, solving problems involving ratios, and finding common denominators.

Can the GCF of 35 and 50 be greater than 5?

No, the GCF of 35 and 50 cannot be greater than 5 because 5 is the largest number that divides both 35 and 50 without leaving a remainder.

How is the GCF of 35 and 50 used in real-life situations?

The GCF is used in real-life situations such as dividing items into smaller sections, comparing quantities, and simplifying mathematical problems involving fractions.

Can the GCF of 35 and 50 be found using a calculator?

Yes, many calculators have a function to find the GCF of two numbers. Simply input the numbers 35 and 50 and use the GCF or GCD function.

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Practice Test

What is the Greatest Common Factor (GCF) of 35 and 50?

5

7

10

15

of 10

Which number is a common factor of both 35 and 50?

2

5

7

10

of 10

How many common factors do 35 and 50 have?

1

2

3

4

of 10

What is the smallest common factor of 35 and 50?

1

5

7

10

of 10

Which of the following is not a common factor of 35 and 50?

1

5

7

10

of 10

The GCF of 35 and 50 is also a factor of which of the following numbers?

5

35

50

All of the above

of 10

If you multiply the GCF of 35 and 50 by 3, what do you get?

10

15

20

30

of 10

Which of the following pairs of numbers has the same GCF as 35 and 50?

30 and 45

50 and 70

35 and 60

70 and 85

of 10

What is the GCF of 35, 50, and 70?

5

10

15

20

of 10

The sum of the GCF of 35 and 50 and the smallest prime number is:

6

7

8

9

of 10

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