Highest Common Factor of 2154, 8840, 77719 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 2154, 8840, 77719 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2154, 8840, 77719 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 2154, 8840, 77719 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 2154, 8840, 77719 is 1.
HCF(2154, 8840, 77719) = 1
HCF of 2154, 8840, 77719 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2154, 8840, 77719 is 1.
Highest Common Factor of 2154,8840,77719 is 1
Step 1: Since 8840 > 2154, we apply the division lemma to 8840 and 2154, to get
8840 = 2154 x 4 + 224
Step 2: Since the reminder 2154 ≠ 0, we apply division lemma to 224 and 2154, to get
2154 = 224 x 9 + 138
Step 3: We consider the new divisor 224 and the new remainder 138, and apply the division lemma to get
224 = 138 x 1 + 86
We consider the new divisor 138 and the new remainder 86,and apply the division lemma to get
138 = 86 x 1 + 52
We consider the new divisor 86 and the new remainder 52,and apply the division lemma to get
86 = 52 x 1 + 34
We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2154 and 8840 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(86,52) = HCF(138,86) = HCF(224,138) = HCF(2154,224) = HCF(8840,2154) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77719 > 2, we apply the division lemma to 77719 and 2, to get
77719 = 2 x 38859 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 77719 is 1
Notice that 1 = HCF(2,1) = HCF(77719,2) .
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Frequently Asked Questions on HCF of 2154, 8840, 77719 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 2154, 8840, 77719?
Answer: HCF of 2154, 8840, 77719 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2154, 8840, 77719 using Euclid's Algorithm?
Answer: For arbitrary numbers 2154, 8840, 77719 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.