Highest Common Factor of 708, 826, 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 708, 826, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 826, 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 708, 826, 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 708, 826, 105 is 1.
HCF(708, 826, 105) = 1
HCF of 708, 826, 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 708, 826, 105 is 1.
Highest Common Factor of 708,826,105 is 1
Step 1: Since 826 > 708, we apply the division lemma to 826 and 708, to get
826 = 708 x 1 + 118
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 118 and 708, to get
708 = 118 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 118, the HCF of 708 and 826 is 118
Notice that 118 = HCF(708,118) = HCF(826,708) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 105, we apply the division lemma to 118 and 105, to get
118 = 105 x 1 + 13
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 13 and 105, to get
105 = 13 x 8 + 1
Step 3: We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 118 and 105 is 1
Notice that 1 = HCF(13,1) = HCF(105,13) = HCF(118,105) .
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Frequently Asked Questions on HCF of 708, 826, 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 708, 826, 105?
Answer: HCF of 708, 826, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 826, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 826, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.