Highest Common Factor of 966, 169, 906, 298 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 966, 169, 906, 298 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 169, 906, 298 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 966, 169, 906, 298 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 966, 169, 906, 298 is 1.
HCF(966, 169, 906, 298) = 1
HCF of 966, 169, 906, 298 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 966, 169, 906, 298 is 1.
Highest Common Factor of 966,169,906,298 is 1
Step 1: Since 966 > 169, we apply the division lemma to 966 and 169, to get
966 = 169 x 5 + 121
Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 121 and 169, to get
169 = 121 x 1 + 48
Step 3: We consider the new divisor 121 and the new remainder 48, and apply the division lemma to get
121 = 48 x 2 + 25
We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get
48 = 25 x 1 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 966 and 169 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(121,48) = HCF(169,121) = HCF(966,169) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 906 > 1, we apply the division lemma to 906 and 1, to get
906 = 1 x 906 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 906 is 1
Notice that 1 = HCF(906,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 298 > 1, we apply the division lemma to 298 and 1, to get
298 = 1 x 298 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 298 is 1
Notice that 1 = HCF(298,1) .
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Frequently Asked Questions on HCF of 966, 169, 906, 298 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 966, 169, 906, 298?
Answer: HCF of 966, 169, 906, 298 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 169, 906, 298 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 169, 906, 298 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.