HCF of 4052 and 420

HCF of 4052 and 420 is the largest possible number that divides 4052 and 420 exactly without any remainder. The factors of 4052 and 420 are 1, 2, 4, 1013, 2026, 4052 and 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 respectively. There are 3 commonly used methods to find the HCF of 4052 and 420 - Euclidean algorithm, prime factorization, and long division.

Answer: HCF of 4052 and 420 is 4.

Explanation:

The HCF of two non-zero integers, x(4052) and y(420), is the highest positive integer m(4) that divides both x(4052) and y(420) without any remainder.

Let's look at the different methods for finding the HCF of 4052 and 420.

• Long Division Method
• Using Euclid's Algorithm
• Prime Factorization Method

HCF of 4052 and 420 by Long Division

HCF of 4052 and 420 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 4052 (larger number) by 420 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (420) by the remainder (272).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 4052 and 420.

HCF of 4052 and 420 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 4052 and Y = 420

• HCF(4052, 420) = HCF(420, 4052 mod 420) = HCF(420, 272)
• HCF(420, 272) = HCF(272, 420 mod 272) = HCF(272, 148)
• HCF(272, 148) = HCF(148, 272 mod 148) = HCF(148, 124)
• HCF(148, 124) = HCF(124, 148 mod 124) = HCF(124, 24)
• HCF(124, 24) = HCF(24, 124 mod 24) = HCF(24, 4)
• HCF(24, 4) = HCF(4, 24 mod 4) = HCF(4, 0)
• HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 4052 and 420 is 4.

HCF of 4052 and 420 by Prime Factorization

Prime factorization of 4052 and 420 is (2 × 2 × 1013) and (2 × 2 × 3 × 5 × 7) respectively. As visible, 4052 and 420 have common prime factors. Hence, the HCF of 4052 and 420 is 2 × 2 = 4.

☛ Also Check:

• HCF of 5 and 10 = 5
• HCF of 84 and 144 = 12
• HCF of 6 and 10 = 2
• HCF of 95 and 152 = 19
• HCF of 34 and 102 = 34
• HCF of 2 and 8 = 2
• HCF of 324 and 144 = 36

FAQs on HCF of 4052 and 420

What is the HCF of 4052 and 420?

The HCF of 4052 and 420 is 4. To calculate the Highest common factor (HCF) of 4052 and 420, we need to factor each number (factors of 4052 = 1, 2, 4, 1013, 2026, 4052; factors of 420 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420) and choose the highest factor that exactly divides both 4052 and 420, i.e., 4.

What is the Relation Between LCM and HCF of 4052, 420?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 4052 and 420, i.e. HCF × LCM = 4052 × 420.

How to Find the HCF of 4052 and 420 by Prime Factorization?

To find the HCF of 4052 and 420, we will find the prime factorization of the given numbers, i.e. 4052 = 2 × 2 × 1013; 420 = 2 × 2 × 3 × 5 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 4052 and 420. Hence, HCF(4052, 420) = 2 × 2 = 4
☛ Prime Numbers

What are the Methods to Find HCF of 4052 and 420?

There are three commonly used methods to find the HCF of 4052 and 420.

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

If the HCF of 420 and 4052 is 4, Find its LCM.

HCF(420, 4052) × LCM(420, 4052) = 420 × 4052
Since the HCF of 420 and 4052 = 4
⇒ 4 × LCM(420, 4052) = 1701840
Therefore, LCM = 425460
☛ Highest Common Factor Calculator

How to Find the HCF of 4052 and 420 by Long Division Method?

To find the HCF of 4052, 420 using long division method, 4052 is divided by 420. The corresponding divisor (4) when remainder equals 0 is taken as HCF.