What is the greatest number that divides 4 and 6 exactly?

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Question 7 Real Numbers Exercise 1.2

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Answer:

From the question, it’s understood that,

445 – 4 = 441, 572 – 5 = 567 and 699 – 6 = 693 has to be exactly divisible by the number. Thus, the required number should be the H.C.F of 441, 567, and 693.

First, consider 441 and 567 and apply Euclid’s division lemma till the remainder becomes 0 567 = 441 x 1 + 126

441 = 126 x 3 + 63

126 = 63 x 2 + 0.

∴ H.C.F (441 and 567) = 63

Next, consider 63 and the third number 693 to apply Euclid’s division lemma

693 = 63 x 11 + 0.

We get, the HCF of 63 and 693 to be 63.

∴ H.C.F. (441, 567 and 693) = 63

So, the required number is 63.

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HCF of 4 and 6 is the largest possible number that divides 4 and 6 exactly without any remainder. The factors of 4 and 6 are 1, 2, 4 and 1, 2, 3, 6 respectively. There are 3 commonly used methods to find the HCF of 4 and 6 - long division, prime factorization, and Euclidean algorithm.

What is HCF of 4 and 6?

Answer: HCF of 4 and 6 is 2.

Explanation:

The HCF of two non-zero integers, x(4) and y(6), is the highest positive integer m(2) that divides both x(4) and y(6) without any remainder.

Methods to Find HCF of 4 and 6

The methods to find the HCF of 4 and 6 are explained below.

• Long Division Method
• Listing Common Factors
• Prime Factorization Method

HCF of 4 and 6 by Long Division

HCF of 4 and 6 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 6 (larger number) by 4 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (2).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 4 and 6.

HCF of 4 and 6 by Listing Common Factors

• Factors of 4: 1, 2, 4
• Factors of 6: 1, 2, 3, 6

There are 2 common factors of 4 and 6, that are 1 and 2. Therefore, the highest common factor of 4 and 6 is 2.

HCF of 4 and 6 by Prime Factorization

Prime factorization of 4 and 6 is (2 × 2) and (2 × 3) respectively. As visible, 4 and 6 have only one common prime factor i.e. 2. Hence, the HCF of 4 and 6 is 2.

☛ Also Check:

1. Example 1: The product of two numbers is 24. If their HCF is 2, what is their LCM?

   Solution:

   Given: HCF = 2 and product of numbers = 24 ∵ LCM × HCF = product of numbers ⇒ LCM = Product/HCF = 24/2

   Therefore, the LCM is 12.

Show Solution >

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The HCF of 4 and 6 is 2. To calculate the HCF (Highest Common Factor) of 4 and 6, we need to factor each number (factors of 4 = 1, 2, 4; factors of 6 = 1, 2, 3, 6) and choose the highest factor that exactly divides both 4 and 6, i.e., 2.

What are the Methods to Find HCF of 4 and 6?

There are three commonly used methods to find the HCF of 4 and 6.

• By Long Division
• By Euclidean Algorithm
• By Prime Factorization

How to Find the HCF of 4 and 6 by Prime Factorization?

To find the HCF of 4 and 6, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 6 = 2 × 3. ⇒ Since 2 is the only common prime factor of 4 and 6. Hence, HCF (4, 6) = 2.

☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 4, 6?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 4 and 6, i.e. HCF × LCM = 4 × 6.

If the HCF of 6 and 4 is 2, Find its LCM.

HCF(6, 4) × LCM(6, 4) = 6 × 4 Since the HCF of 6 and 4 = 2 ⇒ 2 × LCM(6, 4) = 24 Therefore, LCM = 12

☛ HCF Calculator

How to Find the HCF of 4 and 6 by Long Division Method?

To find the HCF of 4, 6 using long division method, 6 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as HCF.