Highest Common Factor of 823, 945, 917, 278 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 823, 945, 917, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 823, 945, 917, 278 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 823, 945, 917, 278 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 823, 945, 917, 278 is 1.
HCF(823, 945, 917, 278) = 1
HCF of 823, 945, 917, 278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 823, 945, 917, 278 is 1.
Highest Common Factor of 823,945,917,278 is 1
Step 1: Since 945 > 823, we apply the division lemma to 945 and 823, to get
945 = 823 x 1 + 122
Step 2: Since the reminder 823 ≠ 0, we apply division lemma to 122 and 823, to get
823 = 122 x 6 + 91
Step 3: We consider the new divisor 122 and the new remainder 91, and apply the division lemma to get
122 = 91 x 1 + 31
We consider the new divisor 91 and the new remainder 31,and apply the division lemma to get
91 = 31 x 2 + 29
We consider the new divisor 31 and the new remainder 29,and apply the division lemma to get
31 = 29 x 1 + 2
We consider the new divisor 29 and the new remainder 2,and apply the division lemma to get
29 = 2 x 14 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 823 and 945 is 1
Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(31,29) = HCF(91,31) = HCF(122,91) = HCF(823,122) = HCF(945,823) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 917 > 1, we apply the division lemma to 917 and 1, to get
917 = 1 x 917 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 917 is 1
Notice that 1 = HCF(917,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 1, we apply the division lemma to 278 and 1, to get
278 = 1 x 278 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 278 is 1
Notice that 1 = HCF(278,1) .
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Frequently Asked Questions on HCF of 823, 945, 917, 278 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 823, 945, 917, 278?
Answer: HCF of 823, 945, 917, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 823, 945, 917, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 823, 945, 917, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.