Highest Common Factor of 561, 902, 171 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 561, 902, 171 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 902, 171 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 561, 902, 171 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 561, 902, 171 is 1.
HCF(561, 902, 171) = 1
HCF of 561, 902, 171 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 902, 171 is 1.
Highest Common Factor of 561,902,171 is 1
Step 1: Since 902 > 561, we apply the division lemma to 902 and 561, to get
902 = 561 x 1 + 341
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 341 and 561, to get
561 = 341 x 1 + 220
Step 3: We consider the new divisor 341 and the new remainder 220, and apply the division lemma to get
341 = 220 x 1 + 121
We consider the new divisor 220 and the new remainder 121,and apply the division lemma to get
220 = 121 x 1 + 99
We consider the new divisor 121 and the new remainder 99,and apply the division lemma to get
121 = 99 x 1 + 22
We consider the new divisor 99 and the new remainder 22,and apply the division lemma to get
99 = 22 x 4 + 11
We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 561 and 902 is 11
Notice that 11 = HCF(22,11) = HCF(99,22) = HCF(121,99) = HCF(220,121) = HCF(341,220) = HCF(561,341) = HCF(902,561) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 171 > 11, we apply the division lemma to 171 and 11, to get
171 = 11 x 15 + 6
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 6 and 11, to get
11 = 6 x 1 + 5
Step 3: We consider the new divisor 6 and the new remainder 5, and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 171 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(171,11) .
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Frequently Asked Questions on HCF of 561, 902, 171 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 561, 902, 171?
Answer: HCF of 561, 902, 171 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 902, 171 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 902, 171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.