Highest Common Factor of 559, 920 using Euclid's algorithm
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 559, 920 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 559, 920 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 559, 920 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 559, 920 is 1.
HCF(559, 920) = 1
HCF of 559, 920 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 559, 920 is 1.
Highest Common Factor of 559,920 is 1
Step 1: Since 920 > 559, we apply the division lemma to 920 and 559, to get
920 = 559 x 1 + 361
Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 361 and 559, to get
559 = 361 x 1 + 198
Step 3: We consider the new divisor 361 and the new remainder 198, and apply the division lemma to get
361 = 198 x 1 + 163
We consider the new divisor 198 and the new remainder 163,and apply the division lemma to get
198 = 163 x 1 + 35
We consider the new divisor 163 and the new remainder 35,and apply the division lemma to get
163 = 35 x 4 + 23
We consider the new divisor 35 and the new remainder 23,and apply the division lemma to get
35 = 23 x 1 + 12
We consider the new divisor 23 and the new remainder 12,and apply the division lemma to get
23 = 12 x 1 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 559 and 920 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(23,12) = HCF(35,23) = HCF(163,35) = HCF(198,163) = HCF(361,198) = HCF(559,361) = HCF(920,559) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 559, 920 using Euclid's Algorithm
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 559, 920?
Answer: HCF of 559, 920 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 559, 920 using Euclid's Algorithm?
Answer: For arbitrary numbers 559, 920 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.