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 562, 363, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 562, 363, 657 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 562, 363, 657 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 562, 363, 657 is 1.
HCF(562, 363, 657) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 562, 363, 657 is 1.
Step 1: Since 562 > 363, we apply the division lemma to 562 and 363, to get
562 = 363 x 1 + 199
Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 199 and 363, to get
363 = 199 x 1 + 164
Step 3: We consider the new divisor 199 and the new remainder 164, and apply the division lemma to get
199 = 164 x 1 + 35
We consider the new divisor 164 and the new remainder 35,and apply the division lemma to get
164 = 35 x 4 + 24
We consider the new divisor 35 and the new remainder 24,and apply the division lemma to get
35 = 24 x 1 + 11
We consider the new divisor 24 and the new remainder 11,and apply the division lemma to get
24 = 11 x 2 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 1
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 562 and 363 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(24,11) = HCF(35,24) = HCF(164,35) = HCF(199,164) = HCF(363,199) = HCF(562,363) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 1, we apply the division lemma to 657 and 1, to get
657 = 1 x 657 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 657 is 1
Notice that 1 = HCF(657,1) .
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 562, 363, 657?
Answer: HCF of 562, 363, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 562, 363, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 562, 363, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.