Highest Common Factor of 840, 695, 55 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 840, 695, 55 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 695, 55 is 5 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 840, 695, 55 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 840, 695, 55 is 5.
HCF(840, 695, 55) = 5
HCF of 840, 695, 55 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 695, 55 is 5.
Highest Common Factor of 840,695,55 is 5
Step 1: Since 840 > 695, we apply the division lemma to 840 and 695, to get
840 = 695 x 1 + 145
Step 2: Since the reminder 695 ≠ 0, we apply division lemma to 145 and 695, to get
695 = 145 x 4 + 115
Step 3: We consider the new divisor 145 and the new remainder 115, and apply the division lemma to get
145 = 115 x 1 + 30
We consider the new divisor 115 and the new remainder 30,and apply the division lemma to get
115 = 30 x 3 + 25
We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get
30 = 25 x 1 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 840 and 695 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(115,30) = HCF(145,115) = HCF(695,145) = HCF(840,695) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 5, we apply the division lemma to 55 and 5, to get
55 = 5 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 55 is 5
Notice that 5 = HCF(55,5) .
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Frequently Asked Questions on HCF of 840, 695, 55 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 840, 695, 55?
Answer: HCF of 840, 695, 55 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 695, 55 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 695, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.