Highest Common Factor of 855, 706, 105 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 855, 706, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 855, 706, 105 is 1 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 855, 706, 105 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 855, 706, 105 is 1.
HCF(855, 706, 105) = 1
HCF of 855, 706, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 855, 706, 105 is 1.
Highest Common Factor of 855,706,105 is 1
Step 1: Since 855 > 706, we apply the division lemma to 855 and 706, to get
855 = 706 x 1 + 149
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 149 and 706, to get
706 = 149 x 4 + 110
Step 3: We consider the new divisor 149 and the new remainder 110, and apply the division lemma to get
149 = 110 x 1 + 39
We consider the new divisor 110 and the new remainder 39,and apply the division lemma to get
110 = 39 x 2 + 32
We consider the new divisor 39 and the new remainder 32,and apply the division lemma to get
39 = 32 x 1 + 7
We consider the new divisor 32 and the new remainder 7,and apply the division lemma to get
32 = 7 x 4 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 855 and 706 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(32,7) = HCF(39,32) = HCF(110,39) = HCF(149,110) = HCF(706,149) = HCF(855,706) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
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Frequently Asked Questions on HCF of 855, 706, 105 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 855, 706, 105?
Answer: HCF of 855, 706, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 855, 706, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 855, 706, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.