Highest Common Factor of 238, 574, 598, 67 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, 574, 598, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 574, 598, 67 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, 574, 598, 67 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, 574, 598, 67 is 1.
HCF(238, 574, 598, 67) = 1
HCF of 238, 574, 598, 67 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, 574, 598, 67 is 1.
Highest Common Factor of 238,574,598,67 is 1
Step 1: Since 574 > 238, we apply the division lemma to 574 and 238, to get
574 = 238 x 2 + 98
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 98 and 238, to get
238 = 98 x 2 + 42
Step 3: We consider the new divisor 98 and the new remainder 42, and apply the division lemma to get
98 = 42 x 2 + 14
We consider the new divisor 42 and the new remainder 14, and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 238 and 574 is 14
Notice that 14 = HCF(42,14) = HCF(98,42) = HCF(238,98) = HCF(574,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 598 > 14, we apply the division lemma to 598 and 14, to get
598 = 14 x 42 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 598 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(598,14) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 2, we apply the division lemma to 67 and 2, to get
67 = 2 x 33 + 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 67 is 1
Notice that 1 = HCF(2,1) = HCF(67,2) .
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Frequently Asked Questions on HCF of 238, 574, 598, 67 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, 574, 598, 67?
Answer: HCF of 238, 574, 598, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 574, 598, 67 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 574, 598, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.