Highest Common Factor of 896, 134, 165, 21 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 896, 134, 165, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 896, 134, 165, 21 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 896, 134, 165, 21 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 896, 134, 165, 21 is 1.
HCF(896, 134, 165, 21) = 1
HCF of 896, 134, 165, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 896, 134, 165, 21 is 1.
Highest Common Factor of 896,134,165,21 is 1
Step 1: Since 896 > 134, we apply the division lemma to 896 and 134, to get
896 = 134 x 6 + 92
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 92 and 134, to get
134 = 92 x 1 + 42
Step 3: We consider the new divisor 92 and the new remainder 42, and apply the division lemma to get
92 = 42 x 2 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 896 and 134 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(92,42) = HCF(134,92) = HCF(896,134) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 165 > 2, we apply the division lemma to 165 and 2, to get
165 = 2 x 82 + 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 165 is 1
Notice that 1 = HCF(2,1) = HCF(165,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
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Frequently Asked Questions on HCF of 896, 134, 165, 21 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 896, 134, 165, 21?
Answer: HCF of 896, 134, 165, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 896, 134, 165, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 896, 134, 165, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.