Highest Common Factor of 910, 689, 870 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 910, 689, 870 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 910, 689, 870 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 910, 689, 870 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 910, 689, 870 is 1.
HCF(910, 689, 870) = 1
HCF of 910, 689, 870 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 910, 689, 870 is 1.
Highest Common Factor of 910,689,870 is 1
Step 1: Since 910 > 689, we apply the division lemma to 910 and 689, to get
910 = 689 x 1 + 221
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 221 and 689, to get
689 = 221 x 3 + 26
Step 3: We consider the new divisor 221 and the new remainder 26, and apply the division lemma to get
221 = 26 x 8 + 13
We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get
26 = 13 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 910 and 689 is 13
Notice that 13 = HCF(26,13) = HCF(221,26) = HCF(689,221) = HCF(910,689) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 13, we apply the division lemma to 870 and 13, to get
870 = 13 x 66 + 12
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 12 and 13, to get
13 = 12 x 1 + 1
Step 3: We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 870 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(870,13) .
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Frequently Asked Questions on HCF of 910, 689, 870 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 910, 689, 870?
Answer: HCF of 910, 689, 870 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 910, 689, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 910, 689, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.