Highest Common Factor of 688, 878, 49, 915 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, 878, 49, 915 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 878, 49, 915 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, 878, 49, 915 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, 878, 49, 915 is 1.
HCF(688, 878, 49, 915) = 1
HCF of 688, 878, 49, 915 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, 878, 49, 915 is 1.
Highest Common Factor of 688,878,49,915 is 1
Step 1: Since 878 > 688, we apply the division lemma to 878 and 688, to get
878 = 688 x 1 + 190
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 190 and 688, to get
688 = 190 x 3 + 118
Step 3: We consider the new divisor 190 and the new remainder 118, and apply the division lemma to get
190 = 118 x 1 + 72
We consider the new divisor 118 and the new remainder 72,and apply the division lemma to get
118 = 72 x 1 + 46
We consider the new divisor 72 and the new remainder 46,and apply the division lemma to get
72 = 46 x 1 + 26
We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get
46 = 26 x 1 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 688 and 878 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(72,46) = HCF(118,72) = HCF(190,118) = HCF(688,190) = HCF(878,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 49 > 2, we apply the division lemma to 49 and 2, to get
49 = 2 x 24 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 49 is 1
Notice that 1 = HCF(2,1) = HCF(49,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 915 > 1, we apply the division lemma to 915 and 1, to get
915 = 1 x 915 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 915 is 1
Notice that 1 = HCF(915,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 688, 878, 49, 915 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, 878, 49, 915?
Answer: HCF of 688, 878, 49, 915 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 878, 49, 915 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 878, 49, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.