Question

The greatest common factor of 14, 21 and 35 is
A.3
B.5
C.7
D.9​

Answer 1

Answer:

The greatest common factor is 7. option C is the correct answer

Explanation:

The Highest Common Factor (HCF) of two or more numbers is the greatest number among all the common factors of the numbers.

From the question, we have

14 = 7×2

21 = 7×3

35 = 7×5

The greatest common factor is 7.

HCF :

The greatest number among all the common factors of the given numbers is known as the Highest Common Factor (HCF) of two or more numbers. Let's look at the numbers 18 and 27 to further understand this. In order to look into this definition, we use the numbers 18 and 27. The elements that both 18 and 27 share are 1, 3, and 9. Nine is the highest (largest) number among these. 18 and 27 have an HCF of 9. The HCF of two or more numbers can be determined by using the prime factorization method.

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Answer 2

The greatest common factor of 14, 21 and 35 is 7

Given :

The numbers 14, 21 and 35

To find :

The greatest common factor of 14, 21 and 35 is

A. 3

B. 5

C. 7

D. 9

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 2 :

Write down the given numbers

Here the given numbers are 14, 21 and 35

Step 2 of 2 :

Prime factorise the given numbers

14 = 2 × 7

21 = 3 × 7

35 = 5 × 7

Step 3 of 3 :

Calculate greatest common factor of 14, 21 and 35

The greatest common factor of 14, 21 and 35 is the greatest number that divides each of the numbers

Since 7 is the greatest number that divides each of the numbers

So the required greatest common factor of 14, 21 and 35 is 7

Hence the correct option is C. 7

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