Highest Common Factor of 665, 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 665, 840 i.e. 35 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 840 is 35 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 665, 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 665, 840 is 35.
HCF(665, 840) = 35
HCF of 665, 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 665, 840 is 35.
Highest Common Factor of 665,840 is 35
Step 1: Since 840 > 665, we apply the division lemma to 840 and 665, to get
840 = 665 x 1 + 175
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 175 and 665, to get
665 = 175 x 3 + 140
Step 3: We consider the new divisor 175 and the new remainder 140, and apply the division lemma to get
175 = 140 x 1 + 35
We consider the new divisor 140 and the new remainder 35, and apply the division lemma to get
140 = 35 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 665 and 840 is 35
Notice that 35 = HCF(140,35) = HCF(175,140) = HCF(665,175) = HCF(840,665) .
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Frequently Asked Questions on HCF of 665, 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 665, 840?
Answer: HCF of 665, 840 is 35 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.