Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 565, 825, 597 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 825, 597 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 565, 825, 597 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 565, 825, 597 is 1.
HCF(565, 825, 597) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 565, 825, 597 is 1.
Step 1: Since 825 > 565, we apply the division lemma to 825 and 565, to get
825 = 565 x 1 + 260
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 260 and 565, to get
565 = 260 x 2 + 45
Step 3: We consider the new divisor 260 and the new remainder 45, and apply the division lemma to get
260 = 45 x 5 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 565 and 825 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(260,45) = HCF(565,260) = HCF(825,565) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 597 > 5, we apply the division lemma to 597 and 5, to get
597 = 5 x 119 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 597 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(597,5) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 565, 825, 597?
Answer: HCF of 565, 825, 597 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 825, 597 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 825, 597 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.