Highest Common Factor of 438, 698, 142 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 438, 698, 142 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 438, 698, 142 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 438, 698, 142 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 438, 698, 142 is 2.
HCF(438, 698, 142) = 2
HCF of 438, 698, 142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 438, 698, 142 is 2.
Highest Common Factor of 438,698,142 is 2
Step 1: Since 698 > 438, we apply the division lemma to 698 and 438, to get
698 = 438 x 1 + 260
Step 2: Since the reminder 438 ≠ 0, we apply division lemma to 260 and 438, to get
438 = 260 x 1 + 178
Step 3: We consider the new divisor 260 and the new remainder 178, and apply the division lemma to get
260 = 178 x 1 + 82
We consider the new divisor 178 and the new remainder 82,and apply the division lemma to get
178 = 82 x 2 + 14
We consider the new divisor 82 and the new remainder 14,and apply the division lemma to get
82 = 14 x 5 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 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 438 and 698 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(82,14) = HCF(178,82) = HCF(260,178) = HCF(438,260) = HCF(698,438) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 142 > 2, we apply the division lemma to 142 and 2, to get
142 = 2 x 71 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 142 is 2
Notice that 2 = HCF(142,2) .
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Frequently Asked Questions on HCF of 438, 698, 142 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 438, 698, 142?
Answer: HCF of 438, 698, 142 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 438, 698, 142 using Euclid's Algorithm?
Answer: For arbitrary numbers 438, 698, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
