Highest Common Factor of 154, 680 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 154, 680 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 154, 680 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 154, 680 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 154, 680 is 2.
HCF(154, 680) = 2
HCF of 154, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 154, 680 is 2.
Highest Common Factor of 154,680 is 2
Step 1: Since 680 > 154, we apply the division lemma to 680 and 154, to get
680 = 154 x 4 + 64
Step 2: Since the reminder 154 ≠ 0, we apply division lemma to 64 and 154, to get
154 = 64 x 2 + 26
Step 3: We consider the new divisor 64 and the new remainder 26, and apply the division lemma to get
64 = 26 x 2 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 154 and 680 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(64,26) = HCF(154,64) = HCF(680,154) .
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Frequently Asked Questions on HCF of 154, 680 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 154, 680?
Answer: HCF of 154, 680 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 154, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 154, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.