HCF of 650 and 1170

The HCF of 650 and 1170 is 130. The prime factorisation, listing common factors, and long division are the three most frequent methods for calculating the HCF of 650 and 1170. The greatest number that divides 650 and 1170 exactly and without leaving a remainder is the HCF of these numbers. 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. 

Also, read: Highest common factor

What is the HCF of 650 and 1170?

The answer to this question is 130. This article shows the HCF of 650 and 1170 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 650 and 1170?

There are three methods to find the HCF of 650 and 1170:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 650 and 1170 by Prime Factorisation Method

The prime factorisation of 650 and 1170 is given by:

Prime factorisation of 650 = (2 x 5 x 5 x 13)

Prime factorisation of 1170 = (2 x 3 x 3 x 5 x 13)

The common prime factors are 2, 5 and 13.

Hence, the HCF of 650 and 1170 = 2 x 5 x 13 = 130.

HCF (650, 1170) = 130

HCF of 650 and 1170 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is the HCF of 650 and 1170.

HCF of 650 and 1170

No further division can be done. 

Hence, HCF (650, 1170) = 130

HCF of 650 and 1170 by Listing Common Factors

To calculate the HCF of 650 and 1170 by listing out the common factors, list the factors as shown below:

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

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HCF of 650 and 1170 Solved Example

Find the highest number that divides 650 and 1170 exactly.

Solution:

The highest number that divides 650 and 1170 exactly is their highest common factor, i.e. HCF of 650 and 1170.

⇒ Factors of 650 and 1170:

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

Therefore, the HCF of 650 and 1170 is 130.

Frequently Asked Questions on HCF of 650 and 1170

Q1

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.
Q2

How to find the HCF of 650 and 1170 by long division method?

To find the HCF of 650 and 1170 using the long division method, 1170 is divided by 650. The corresponding divisor (130) when remainder equals 0 is taken as HCF.
Q3

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. They are:
Long Division
Listing Common Factors
Prime Factorisation
Q4

How to find the HCF of 650 and 1170 by prime factorisation?

To find the HCF of 650 and 1170, we will find the prime factorisation of the given numbers, i.e. 650 = 2 × 5 × 5 × 13; 1170 = 2 × 3 × 3 × 5 × 13.
⇒ Since 2, 5 and 13 are common terms in the prime factorisation of 650 and 1170, HCF(650, 1170) = 2 × 5 × 13 = 130
Q5

What is the relation between LCM and HCF of 650, 1170?

The following equation can be used to express the relation between LCM and HCF of 650 and 1170, i.e. HCF × LCM = 650 × 1170 = 760500.

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