Highest Common Factor of 688, 899, 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 688, 899, 870 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 899, 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 688, 899, 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 688, 899, 870 is 1.
HCF(688, 899, 870) = 1
HCF of 688, 899, 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 688, 899, 870 is 1.
Highest Common Factor of 688,899,870 is 1
Step 1: Since 899 > 688, we apply the division lemma to 899 and 688, to get
899 = 688 x 1 + 211
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 211 and 688, to get
688 = 211 x 3 + 55
Step 3: We consider the new divisor 211 and the new remainder 55, and apply the division lemma to get
211 = 55 x 3 + 46
We consider the new divisor 55 and the new remainder 46,and apply the division lemma to get
55 = 46 x 1 + 9
We consider the new divisor 46 and the new remainder 9,and apply the division lemma to get
46 = 9 x 5 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 688 and 899 is 1
Notice that 1 = HCF(9,1) = HCF(46,9) = HCF(55,46) = HCF(211,55) = HCF(688,211) = HCF(899,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 1, we apply the division lemma to 870 and 1, to get
870 = 1 x 870 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 870 is 1
Notice that 1 = HCF(870,1) .
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Frequently Asked Questions on HCF of 688, 899, 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 688, 899, 870?
Answer: HCF of 688, 899, 870 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 899, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 899, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.