Highest Common Factor of 492, 668, 342 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 492, 668, 342 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 492, 668, 342 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 492, 668, 342 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 492, 668, 342 is 2.
HCF(492, 668, 342) = 2
HCF of 492, 668, 342 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 492, 668, 342 is 2.
Highest Common Factor of 492,668,342 is 2
Step 1: Since 668 > 492, we apply the division lemma to 668 and 492, to get
668 = 492 x 1 + 176
Step 2: Since the reminder 492 ≠ 0, we apply division lemma to 176 and 492, to get
492 = 176 x 2 + 140
Step 3: We consider the new divisor 176 and the new remainder 140, and apply the division lemma to get
176 = 140 x 1 + 36
We consider the new divisor 140 and the new remainder 36,and apply the division lemma to get
140 = 36 x 3 + 32
We consider the new divisor 36 and the new remainder 32,and apply the division lemma to get
36 = 32 x 1 + 4
We consider the new divisor 32 and the new remainder 4,and apply the division lemma to get
32 = 4 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 492 and 668 is 4
Notice that 4 = HCF(32,4) = HCF(36,32) = HCF(140,36) = HCF(176,140) = HCF(492,176) = HCF(668,492) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 4, we apply the division lemma to 342 and 4, to get
342 = 4 x 85 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 342 is 2
Notice that 2 = HCF(4,2) = HCF(342,4) .
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Frequently Asked Questions on HCF of 492, 668, 342 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 492, 668, 342?
Answer: HCF of 492, 668, 342 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 492, 668, 342 using Euclid's Algorithm?
Answer: For arbitrary numbers 492, 668, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.