The HCF of 777, 315 and 588 is 21. The largest number, which is the factor of two or more numbers, is called the Highest Common Factor (HCF). It is the largest positive integer that divides the given numbers without leaving a remainder. The number 21 divides the numbers 777, 315 and 588 exactly. Hence, the Highest Common Factor of 777, 315 and 588 is 21. For more conceptual knowledge, follow the article HCF, which has been curated by experts in simple and understandable language. Learn the tricks of solving problems based on HCF with the help of solved examples and FAQs in a detailed manner here.
What is the HCF of 777, 315 and 588?
The Highest Common Factor of 777, 315 and 588 is 21. Thus, the number that divides the numbers 777, 315 and 588 is 21. We learn the simple tricks on how to find the Highest Common Factor using various methods here.
How to Find HCF of 777, 315 and 588?
There are three methods to find the HCF of 777, 315 and 588:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 777, 315 and 588 by Prime Factorisation Method
In the prime factorisation method, we express the numbers as the product of prime factors. Hence the given numbers 777, 315 and 588 are written as:
777 = 3 × 7 × 37
315 = 3 × 3 × 5 × 7
588 = 2 × 2 × 3 × 7 × 7
The Common prime factors of 777, 315 and 588 are 3 and 7.
Therefore,
HCF (777, 315, 588) = 3 × 7 = 21
HCF of 777, 315 and 588 by Long Division Method
In the long division method, we use the following steps to determine the HCF of 777, 315 and 588.
Step 1: Divide the number 777 by 315. We get the divisor as 21 when the remainder is zero. Hence, the HCF of 777 and 315 is 21.
Step 2: Now, perform the division process on 21 and 588 to calculate the HCF.
Step 3: Here, we get the divisor as 21 when the remainder is zero. Thus the HCF of 21 and 588 is 21.
The HCF of 777, 315 and 588 by the long division method is shown below.
First, divide the number 777 by 315
The HCF of 777 and 315 is 21.
Now, divide the number 588 by 21.
The HCF of 21 and 588 is 21.
Hence, HCF (777, 315, 588) = 21
HCF of 777, 315 and 588 by Listing Common Factors
We need to list out the factors of 777, 315 and 588 to find their HCF in this method. The factors of 777, 315 and 588 are given below:
Factors of 777: 1, 3, 7, 21, 37, 111, 259, 777
Factors of 315: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
Factors of 588: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
Hence, HCF (777, 315, 588) = 21
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Solved Example
Question: What is the highest number that divides 777, 315 and 588 exactly?
Solution: The HCF of 777, 315 and 588 is the highest number that divides 777, 315 and 588 exactly. We need to list the factors of the given numbers to find the HCF.
Factors of 777: 1, 3, 7, 21, 37, 111, 259, 777
Factors of 315: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
Factors of 588: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
Therefore the Highest Common Factor of 777, 315 and 588 is 21.
Frequently Asked Questions on HCF of 777, 315 and 588
What is the HCF of 777, 315 and 588?
How to find the HCF of 777, 315 and 588 by prime factorisation?
In this method, we express the given numbers as the product of prime factors. Therefore, the numbers 777, 315 and 588 can be expressed as:
777 = 3 × 7 × 37
315 = 3 × 3 × 5 × 7
588 = 2 × 2 × 3 × 7 × 7
Common prime factors of 777, 315 and 588 are 3 and 7
Therefore, HCF (777, 315, 588) = 3 × 7 = 21
Mention the methods to find the HCF of 777, 315 and 588.
The methods used to find the HCF of 777, 315 and 588 are:
Prime Factorisation
Long Division method
Listing common factors
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