Highest Common Factor of 180, 154, 668 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 180, 154, 668 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 180, 154, 668 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 180, 154, 668 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 180, 154, 668 is 2.
HCF(180, 154, 668) = 2
HCF of 180, 154, 668 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 180, 154, 668 is 2.
Highest Common Factor of 180,154,668 is 2
Step 1: Since 180 > 154, we apply the division lemma to 180 and 154, to get
180 = 154 x 1 + 26
Step 2: Since the reminder 154 ≠ 0, we apply division lemma to 26 and 154, to get
154 = 26 x 5 + 24
Step 3: We consider the new divisor 26 and the new remainder 24, and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2, and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 180 and 154 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(154,26) = HCF(180,154) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 668 > 2, we apply the division lemma to 668 and 2, to get
668 = 2 x 334 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 668 is 2
Notice that 2 = HCF(668,2) .
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Frequently Asked Questions on HCF of 180, 154, 668 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 180, 154, 668?
Answer: HCF of 180, 154, 668 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 180, 154, 668 using Euclid's Algorithm?
Answer: For arbitrary numbers 180, 154, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
