Highest Common Factor of 664, 856 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 664, 856 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 856 is 8 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 664, 856 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 664, 856 is 8.
HCF(664, 856) = 8
HCF of 664, 856 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 856 is 8.
Highest Common Factor of 664,856 is 8
Step 1: Since 856 > 664, we apply the division lemma to 856 and 664, to get
856 = 664 x 1 + 192
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 192 and 664, to get
664 = 192 x 3 + 88
Step 3: We consider the new divisor 192 and the new remainder 88, and apply the division lemma to get
192 = 88 x 2 + 16
We consider the new divisor 88 and the new remainder 16,and apply the division lemma to get
88 = 16 x 5 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 664 and 856 is 8
Notice that 8 = HCF(16,8) = HCF(88,16) = HCF(192,88) = HCF(664,192) = HCF(856,664) .
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Frequently Asked Questions on HCF of 664, 856 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 664, 856?
Answer: HCF of 664, 856 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 856 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 856 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.