Highest Common Factor of 1944, 3294, 39412 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 1944, 3294, 39412 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1944, 3294, 39412 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 1944, 3294, 39412 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 1944, 3294, 39412 is 2.
HCF(1944, 3294, 39412) = 2
HCF of 1944, 3294, 39412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1944, 3294, 39412 is 2.
Highest Common Factor of 1944,3294,39412 is 2
Step 1: Since 3294 > 1944, we apply the division lemma to 3294 and 1944, to get
3294 = 1944 x 1 + 1350
Step 2: Since the reminder 1944 ≠ 0, we apply division lemma to 1350 and 1944, to get
1944 = 1350 x 1 + 594
Step 3: We consider the new divisor 1350 and the new remainder 594, and apply the division lemma to get
1350 = 594 x 2 + 162
We consider the new divisor 594 and the new remainder 162,and apply the division lemma to get
594 = 162 x 3 + 108
We consider the new divisor 162 and the new remainder 108,and apply the division lemma to get
162 = 108 x 1 + 54
We consider the new divisor 108 and the new remainder 54,and apply the division lemma to get
108 = 54 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 1944 and 3294 is 54
Notice that 54 = HCF(108,54) = HCF(162,108) = HCF(594,162) = HCF(1350,594) = HCF(1944,1350) = HCF(3294,1944) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39412 > 54, we apply the division lemma to 39412 and 54, to get
39412 = 54 x 729 + 46
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 46 and 54, to get
54 = 46 x 1 + 8
Step 3: We consider the new divisor 46 and the new remainder 8, and apply the division lemma to get
46 = 8 x 5 + 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 54 and 39412 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(46,8) = HCF(54,46) = HCF(39412,54) .
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Frequently Asked Questions on HCF of 1944, 3294, 39412 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 1944, 3294, 39412?
Answer: HCF of 1944, 3294, 39412 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1944, 3294, 39412 using Euclid's Algorithm?
Answer: For arbitrary numbers 1944, 3294, 39412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
