Highest Common Factor of 784, 644, 42 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 784, 644, 42 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 644, 42 is 14 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 784, 644, 42 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 784, 644, 42 is 14.
HCF(784, 644, 42) = 14
HCF of 784, 644, 42 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 784, 644, 42 is 14.
Highest Common Factor of 784,644,42 is 14
Step 1: Since 784 > 644, we apply the division lemma to 784 and 644, to get
784 = 644 x 1 + 140
Step 2: Since the reminder 644 ≠ 0, we apply division lemma to 140 and 644, to get
644 = 140 x 4 + 84
Step 3: We consider the new divisor 140 and the new remainder 84, and apply the division lemma to get
140 = 84 x 1 + 56
We consider the new divisor 84 and the new remainder 56,and apply the division lemma to get
84 = 56 x 1 + 28
We consider the new divisor 56 and the new remainder 28,and apply the division lemma to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 784 and 644 is 28
Notice that 28 = HCF(56,28) = HCF(84,56) = HCF(140,84) = HCF(644,140) = HCF(784,644) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 28, we apply the division lemma to 42 and 28, to get
42 = 28 x 1 + 14
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 14 and 28, to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 28 and 42 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) .
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Frequently Asked Questions on HCF of 784, 644, 42 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 784, 644, 42?
Answer: HCF of 784, 644, 42 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 644, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 644, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
