Highest Common Factor of 714, 4158, 6046 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 714, 4158, 6046 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 4158, 6046 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 714, 4158, 6046 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 714, 4158, 6046 is 2.
HCF(714, 4158, 6046) = 2
HCF of 714, 4158, 6046 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 4158, 6046 is 2.
Highest Common Factor of 714,4158,6046 is 2
Step 1: Since 4158 > 714, we apply the division lemma to 4158 and 714, to get
4158 = 714 x 5 + 588
Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 588 and 714, to get
714 = 588 x 1 + 126
Step 3: We consider the new divisor 588 and the new remainder 126, and apply the division lemma to get
588 = 126 x 4 + 84
We consider the new divisor 126 and the new remainder 84,and apply the division lemma to get
126 = 84 x 1 + 42
We consider the new divisor 84 and the new remainder 42,and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 714 and 4158 is 42
Notice that 42 = HCF(84,42) = HCF(126,84) = HCF(588,126) = HCF(714,588) = HCF(4158,714) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6046 > 42, we apply the division lemma to 6046 and 42, to get
6046 = 42 x 143 + 40
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 40 and 42, to get
42 = 40 x 1 + 2
Step 3: We consider the new divisor 40 and the new remainder 2, and apply the division lemma to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 42 and 6046 is 2
Notice that 2 = HCF(40,2) = HCF(42,40) = HCF(6046,42) .
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Frequently Asked Questions on HCF of 714, 4158, 6046 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 714, 4158, 6046?
Answer: HCF of 714, 4158, 6046 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 4158, 6046 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 4158, 6046 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.