Highest Common Factor of 664, 840 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, 840 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 840 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, 840 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, 840 is 8.
HCF(664, 840) = 8
HCF of 664, 840 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, 840 is 8.
Highest Common Factor of 664,840 is 8
Step 1: Since 840 > 664, we apply the division lemma to 840 and 664, to get
840 = 664 x 1 + 176
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 176 and 664, to get
664 = 176 x 3 + 136
Step 3: We consider the new divisor 176 and the new remainder 136, and apply the division lemma to get
176 = 136 x 1 + 40
We consider the new divisor 136 and the new remainder 40,and apply the division lemma to get
136 = 40 x 3 + 16
We consider the new divisor 40 and the new remainder 16,and apply the division lemma to get
40 = 16 x 2 + 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 840 is 8
Notice that 8 = HCF(16,8) = HCF(40,16) = HCF(136,40) = HCF(176,136) = HCF(664,176) = HCF(840,664) .
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Frequently Asked Questions on HCF of 664, 840 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, 840?
Answer: HCF of 664, 840 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.