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 569, 912, 270, 43 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 569, 912, 270, 43 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 569, 912, 270, 43 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 569, 912, 270, 43 is 1.
HCF(569, 912, 270, 43) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 569, 912, 270, 43 is 1.
Step 1: Since 912 > 569, we apply the division lemma to 912 and 569, to get
912 = 569 x 1 + 343
Step 2: Since the reminder 569 ≠ 0, we apply division lemma to 343 and 569, to get
569 = 343 x 1 + 226
Step 3: We consider the new divisor 343 and the new remainder 226, and apply the division lemma to get
343 = 226 x 1 + 117
We consider the new divisor 226 and the new remainder 117,and apply the division lemma to get
226 = 117 x 1 + 109
We consider the new divisor 117 and the new remainder 109,and apply the division lemma to get
117 = 109 x 1 + 8
We consider the new divisor 109 and the new remainder 8,and apply the division lemma to get
109 = 8 x 13 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 569 and 912 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(109,8) = HCF(117,109) = HCF(226,117) = HCF(343,226) = HCF(569,343) = HCF(912,569) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 1, we apply the division lemma to 270 and 1, to get
270 = 1 x 270 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 270 is 1
Notice that 1 = HCF(270,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43 > 1, we apply the division lemma to 43 and 1, to get
43 = 1 x 43 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 43 is 1
Notice that 1 = HCF(43,1) .
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 569, 912, 270, 43?
Answer: HCF of 569, 912, 270, 43 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 569, 912, 270, 43 using Euclid's Algorithm?
Answer: For arbitrary numbers 569, 912, 270, 43 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.