Highest Common Factor of 668, 800, 34 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 668, 800, 34 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 668, 800, 34 is 2 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 668, 800, 34 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 668, 800, 34 is 2.
HCF(668, 800, 34) = 2
HCF of 668, 800, 34 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 668, 800, 34 is 2.
Highest Common Factor of 668,800,34 is 2
Step 1: Since 800 > 668, we apply the division lemma to 800 and 668, to get
800 = 668 x 1 + 132
Step 2: Since the reminder 668 ≠ 0, we apply division lemma to 132 and 668, to get
668 = 132 x 5 + 8
Step 3: We consider the new divisor 132 and the new remainder 8, and apply the division lemma to get
132 = 8 x 16 + 4
We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 668 and 800 is 4
Notice that 4 = HCF(8,4) = HCF(132,8) = HCF(668,132) = HCF(800,668) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34 > 4, we apply the division lemma to 34 and 4, to get
34 = 4 x 8 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 34 is 2
Notice that 2 = HCF(4,2) = HCF(34,4) .
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Frequently Asked Questions on HCF of 668, 800, 34 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 668, 800, 34?
Answer: HCF of 668, 800, 34 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 668, 800, 34 using Euclid's Algorithm?
Answer: For arbitrary numbers 668, 800, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.