Highest Common Factor of 142, 680, 824 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 142, 680, 824 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 142, 680, 824 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 142, 680, 824 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 142, 680, 824 is 2.
HCF(142, 680, 824) = 2
HCF of 142, 680, 824 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 142, 680, 824 is 2.
Highest Common Factor of 142,680,824 is 2
Step 1: Since 680 > 142, we apply the division lemma to 680 and 142, to get
680 = 142 x 4 + 112
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 112 and 142, to get
142 = 112 x 1 + 30
Step 3: We consider the new divisor 112 and the new remainder 30, and apply the division lemma to get
112 = 30 x 3 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 142 and 680 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(112,30) = HCF(142,112) = HCF(680,142) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 824 > 2, we apply the division lemma to 824 and 2, to get
824 = 2 x 412 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 824 is 2
Notice that 2 = HCF(824,2) .
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Frequently Asked Questions on HCF of 142, 680, 824 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 142, 680, 824?
Answer: HCF of 142, 680, 824 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 142, 680, 824 using Euclid's Algorithm?
Answer: For arbitrary numbers 142, 680, 824 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.