Highest Common Factor of 218, 142, 769, 916 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 218, 142, 769, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 218, 142, 769, 916 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 218, 142, 769, 916 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 218, 142, 769, 916 is 1.
HCF(218, 142, 769, 916) = 1
HCF of 218, 142, 769, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 218, 142, 769, 916 is 1.
Highest Common Factor of 218,142,769,916 is 1
Step 1: Since 218 > 142, we apply the division lemma to 218 and 142, to get
218 = 142 x 1 + 76
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 76 and 142, to get
142 = 76 x 1 + 66
Step 3: We consider the new divisor 76 and the new remainder 66, and apply the division lemma to get
76 = 66 x 1 + 10
We consider the new divisor 66 and the new remainder 10,and apply the division lemma to get
66 = 10 x 6 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 218 and 142 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(76,66) = HCF(142,76) = HCF(218,142) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 769 > 2, we apply the division lemma to 769 and 2, to get
769 = 2 x 384 + 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 769 is 1
Notice that 1 = HCF(2,1) = HCF(769,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 916 > 1, we apply the division lemma to 916 and 1, to get
916 = 1 x 916 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 916 is 1
Notice that 1 = HCF(916,1) .
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Frequently Asked Questions on HCF of 218, 142, 769, 916 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 218, 142, 769, 916?
Answer: HCF of 218, 142, 769, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 218, 142, 769, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 218, 142, 769, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.