Highest Common Factor of 42, 274, 344, 434 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 42, 274, 344, 434 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 42, 274, 344, 434 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 42, 274, 344, 434 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 42, 274, 344, 434 is 2.
HCF(42, 274, 344, 434) = 2
HCF of 42, 274, 344, 434 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 42, 274, 344, 434 is 2.
Highest Common Factor of 42,274,344,434 is 2
Step 1: Since 274 > 42, we apply the division lemma to 274 and 42, to get
274 = 42 x 6 + 22
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 22 and 42, to get
42 = 22 x 1 + 20
Step 3: We consider the new divisor 22 and the new remainder 20, and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2, and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 42 and 274 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(274,42) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 344 > 2, we apply the division lemma to 344 and 2, to get
344 = 2 x 172 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 344 is 2
Notice that 2 = HCF(344,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 434 > 2, we apply the division lemma to 434 and 2, to get
434 = 2 x 217 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 434 is 2
Notice that 2 = HCF(434,2) .
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Frequently Asked Questions on HCF of 42, 274, 344, 434 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 42, 274, 344, 434?
Answer: HCF of 42, 274, 344, 434 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 42, 274, 344, 434 using Euclid's Algorithm?
Answer: For arbitrary numbers 42, 274, 344, 434 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.