HCF of 506 and 1155

The HCF of 506 and 1155 is 11. The Highest Common Factor (HCF) is defined as the largest positive integer that divides two or more numbers evenly. This concept is one of the most vital concepts in Mathematics. Hence, teachers suggest students learn the concept thoroughly and obtain excellent marks in exams. The article HCF is well-structured by subject experts in a simple language, with the aim of making students’ learning process easy and effective. In this article, we will learn the simple procedure of how to find the Highest Common Factor of 506 and 1155 using prime factorisation, long division method and listing common factors.

What is the HCF of 506 and 1155?

The answer to this question is 11. The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506, and the factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155. Among the factors of 506 and 1155, the highest common number is 11. Therefore, the Highest Common Factor of 506 and 1155 is 11.

How to Find HCF of 506 and 1155?

Let us have a look at the methods used to find the HCF of 506 and 1155 given below:

• Prime Factorisation
• Long Division method
• Listing common factors

HCF of 506 and 1155 by Prime Factorisation Method

In this method, we express the numbers as the product of prime factors. To determine the Highest Common Factor, multiply all the common prime factors with the lowest degree (power).

506 = 2 × 11 × 23

1155 = 3 × 5 × 7 × 11

The common prime factor of 506 and 1155 is 11.

Therefore,

HCF of (506, 1155) = 11

HCF of 506 and 1155 by Long Division Method

The steps mentioned below are used to find the Highest Common Factor of 506 and 1155:

Step 1: Divide the largest number by the smallest number from the given two numbers.

Step 2: Now, check the remainder. If it is not 0, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.

Step 3: Continue this process until we get the remainder as zero. The last divisor will be the HCF of the given two numbers.

The HCF of 506 and 1155 by the long division method is as follows:

Hence, HCF (506, 1155) = 11

HCF of 506 and 1155 by Listing Common Factors

Here, we can find the Highest Common Factor by listing all the factors of given numbers. The factors of 506 and 1155 are as follows:

Factors of 506: 1, 2, 11, 22, 23, 46, 253, 506

Factors of 1155: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155

Hence, HCF (506, 1155) = 11

Related Articles

• Highest Common Factor
• GCF
• HCF and LCM
• HCF of Two Numbers
• GCF Calculator

Video Lesson on Properties of HCF and LCM

Solved Example

Question: What is the highest number that divides both 506 and 1155 exactly?

Solution: The highest number that divides both 506 and 1155 is their Highest Common Factor. Let us list the factors of 506 and 1155 to find the HCF.

Factors of 506: 1, 2, 11, 22, 23, 46, 253, 506

Factors of 1155: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155

Here, 11 is the Highest Common Factor. Therefore, the highest number that divides both 506 and 1155 is 11.