Highest Common Factor of 238, 358, 709 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 238, 358, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 358, 709 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 238, 358, 709 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 238, 358, 709 is 1.
HCF(238, 358, 709) = 1
HCF of 238, 358, 709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 238, 358, 709 is 1.
Highest Common Factor of 238,358,709 is 1
Step 1: Since 358 > 238, we apply the division lemma to 358 and 238, to get
358 = 238 x 1 + 120
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 120 and 238, to get
238 = 120 x 1 + 118
Step 3: We consider the new divisor 120 and the new remainder 118, and apply the division lemma to get
120 = 118 x 1 + 2
We consider the new divisor 118 and the new remainder 2, and apply the division lemma to get
118 = 2 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 238 and 358 is 2
Notice that 2 = HCF(118,2) = HCF(120,118) = HCF(238,120) = HCF(358,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 2, we apply the division lemma to 709 and 2, to get
709 = 2 x 354 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 709 is 1
Notice that 1 = HCF(2,1) = HCF(709,2) .
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Frequently Asked Questions on HCF of 238, 358, 709 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 238, 358, 709?
Answer: HCF of 238, 358, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 358, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 358, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.