Highest Common Factor of 340, 660, 754 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 340, 660, 754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 660, 754 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 340, 660, 754 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 340, 660, 754 is 2.
HCF(340, 660, 754) = 2
HCF of 340, 660, 754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 660, 754 is 2.
Highest Common Factor of 340,660,754 is 2
Step 1: Since 660 > 340, we apply the division lemma to 660 and 340, to get
660 = 340 x 1 + 320
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 320 and 340, to get
340 = 320 x 1 + 20
Step 3: We consider the new divisor 320 and the new remainder 20, and apply the division lemma to get
320 = 20 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 340 and 660 is 20
Notice that 20 = HCF(320,20) = HCF(340,320) = HCF(660,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 754 > 20, we apply the division lemma to 754 and 20, to get
754 = 20 x 37 + 14
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 14 and 20, to get
20 = 14 x 1 + 6
Step 3: We consider the new divisor 14 and the new remainder 6, and apply the division lemma to get
14 = 6 x 2 + 2
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 20 and 754 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(754,20) .
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Frequently Asked Questions on HCF of 340, 660, 754 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 340, 660, 754?
Answer: HCF of 340, 660, 754 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 660, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 660, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.