Highest Common Factor of 140, 357, 614 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 140, 357, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 140, 357, 614 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 140, 357, 614 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 140, 357, 614 is 1.
HCF(140, 357, 614) = 1
HCF of 140, 357, 614 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 140, 357, 614 is 1.
Highest Common Factor of 140,357,614 is 1
Step 1: Since 357 > 140, we apply the division lemma to 357 and 140, to get
357 = 140 x 2 + 77
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 77 and 140, to get
140 = 77 x 1 + 63
Step 3: We consider the new divisor 77 and the new remainder 63, and apply the division lemma to get
77 = 63 x 1 + 14
We consider the new divisor 63 and the new remainder 14,and apply the division lemma to get
63 = 14 x 4 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 140 and 357 is 7
Notice that 7 = HCF(14,7) = HCF(63,14) = HCF(77,63) = HCF(140,77) = HCF(357,140) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 614 > 7, we apply the division lemma to 614 and 7, to get
614 = 7 x 87 + 5
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get
7 = 5 x 1 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 7 and 614 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(614,7) .
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Frequently Asked Questions on HCF of 140, 357, 614 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 140, 357, 614?
Answer: HCF of 140, 357, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 140, 357, 614 using Euclid's Algorithm?
Answer: For arbitrary numbers 140, 357, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.