HCF of 650 and 1170

HCF of 650 and 1170 is the largest possible number that divides 650 and 1170 exactly without any remainder. The factors of 650 and 1170 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 and 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, 1170 respectively. There are 3 commonly used methods to find the HCF of 650 and 1170 - long division, Euclidean algorithm, and prime factorization.

Answer: HCF of 650 and 1170 is 130.

Explanation:

The HCF of two non-zero integers, x(650) and y(1170), is the highest positive integer m(130) that divides both x(650) and y(1170) without any remainder.

The methods to find the HCF of 650 and 1170 are explained below.

• Long Division Method
• Listing Common Factors
• Using Euclid's Algorithm

HCF of 650 and 1170 by Long Division

HCF of 650 and 1170 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 1170 (larger number) by 650 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (650) by the remainder (520).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (130) is the HCF of 650 and 1170.

HCF of 650 and 1170 by Listing Common Factors

• Factors of 650: 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650
• Factors of 1170: 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, 1170

There are 8 common factors of 650 and 1170, that are 65, 1, 2, 130, 5, 10, 13, and 26. Therefore, the highest common factor of 650 and 1170 is 130.

HCF of 650 and 1170 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 = 1170 and Y = 650

• HCF(1170, 650) = HCF(650, 1170 mod 650) = HCF(650, 520)
• HCF(650, 520) = HCF(520, 650 mod 520) = HCF(520, 130)
• HCF(520, 130) = HCF(130, 520 mod 130) = HCF(130, 0)
• HCF(130, 0) = 130 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 650 and 1170 is 130.

☛ Also Check:

• HCF of 65 and 117 = 13
• HCF of 612 and 1314 = 18
• HCF of 16 and 27 = 1
• HCF of 84 and 120 = 12
• HCF of 70, 105 and 175 = 35
• HCF of 12 and 16 = 4
• HCF of 12, 45 and 75 = 3

FAQs on HCF of 650 and 1170

What is the HCF of 650 and 1170?

The HCF of 650 and 1170 is 130. To calculate the Highest common factor (HCF) of 650 and 1170, we need to factor each number (factors of 650 = 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650; factors of 1170 = 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, 1170) and choose the highest factor that exactly divides both 650 and 1170, i.e., 130.

What are the Methods to Find HCF of 650 and 1170?

There are three commonly used methods to find the HCF of 650 and 1170.

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

How to Find the HCF of 650 and 1170 by Long Division Method?

To find the HCF of 650, 1170 using long division method, 1170 is divided by 650. The corresponding divisor (130) when remainder equals 0 is taken as HCF.

How to Find the HCF of 650 and 1170 by Prime Factorization?

To find the HCF of 650 and 1170, we will find the prime factorization of the given numbers, i.e. 650 = 2 × 5 × 5 × 13; 1170 = 2 × 3 × 3 × 5 × 13.
⇒ Since 2, 5, 13 are common terms in the prime factorization of 650 and 1170. Hence, HCF(650, 1170) = 2 × 5 × 13 = 130
☛ What is a Prime Number?

If the HCF of 1170 and 650 is 130, Find its LCM.

HCF(1170, 650) × LCM(1170, 650) = 1170 × 650
Since the HCF of 1170 and 650 = 130
⇒ 130 × LCM(1170, 650) = 760500
Therefore, LCM = 5850
☛ HCF Calculator

What is the Relation Between LCM and HCF of 650, 1170?

The following equation can be used to express the relation between Least Common Multiple and HCF of 650 and 1170, i.e. HCF × LCM = 650 × 1170.