Highest Common Factor of 342, 648, 874 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 342, 648, 874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 648, 874 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 342, 648, 874 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 342, 648, 874 is 2.
HCF(342, 648, 874) = 2
HCF of 342, 648, 874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 648, 874 is 2.
Highest Common Factor of 342,648,874 is 2
Step 1: Since 648 > 342, we apply the division lemma to 648 and 342, to get
648 = 342 x 1 + 306
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 306 and 342, to get
342 = 306 x 1 + 36
Step 3: We consider the new divisor 306 and the new remainder 36, and apply the division lemma to get
306 = 36 x 8 + 18
We consider the new divisor 36 and the new remainder 18, and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 342 and 648 is 18
Notice that 18 = HCF(36,18) = HCF(306,36) = HCF(342,306) = HCF(648,342) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 18, we apply the division lemma to 874 and 18, to get
874 = 18 x 48 + 10
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 10 and 18, to get
18 = 10 x 1 + 8
Step 3: We consider the new divisor 10 and the new remainder 8, and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 874 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(874,18) .
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Frequently Asked Questions on HCF of 342, 648, 874 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 342, 648, 874?
Answer: HCF of 342, 648, 874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 648, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 648, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.