Highest Common Factor of 608, 992, 166 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 608, 992, 166 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 992, 166 is 2 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 608, 992, 166 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 608, 992, 166 is 2.
HCF(608, 992, 166) = 2
HCF of 608, 992, 166 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 992, 166 is 2.
Highest Common Factor of 608,992,166 is 2
Step 1: Since 992 > 608, we apply the division lemma to 992 and 608, to get
992 = 608 x 1 + 384
Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 384 and 608, to get
608 = 384 x 1 + 224
Step 3: We consider the new divisor 384 and the new remainder 224, and apply the division lemma to get
384 = 224 x 1 + 160
We consider the new divisor 224 and the new remainder 160,and apply the division lemma to get
224 = 160 x 1 + 64
We consider the new divisor 160 and the new remainder 64,and apply the division lemma to get
160 = 64 x 2 + 32
We consider the new divisor 64 and the new remainder 32,and apply the division lemma to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 608 and 992 is 32
Notice that 32 = HCF(64,32) = HCF(160,64) = HCF(224,160) = HCF(384,224) = HCF(608,384) = HCF(992,608) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 166 > 32, we apply the division lemma to 166 and 32, to get
166 = 32 x 5 + 6
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 6 and 32, to get
32 = 6 x 5 + 2
Step 3: 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 32 and 166 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(166,32) .
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Frequently Asked Questions on HCF of 608, 992, 166 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 608, 992, 166?
Answer: HCF of 608, 992, 166 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 992, 166 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 992, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.