Highest Common Factor of 454, 784, 22 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 454, 784, 22 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 454, 784, 22 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 454, 784, 22 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 454, 784, 22 is 2.
HCF(454, 784, 22) = 2
HCF of 454, 784, 22 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 454, 784, 22 is 2.
Highest Common Factor of 454,784,22 is 2
Step 1: Since 784 > 454, we apply the division lemma to 784 and 454, to get
784 = 454 x 1 + 330
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 330 and 454, to get
454 = 330 x 1 + 124
Step 3: We consider the new divisor 330 and the new remainder 124, and apply the division lemma to get
330 = 124 x 2 + 82
We consider the new divisor 124 and the new remainder 82,and apply the division lemma to get
124 = 82 x 1 + 42
We consider the new divisor 82 and the new remainder 42,and apply the division lemma to get
82 = 42 x 1 + 40
We consider the new divisor 42 and the new remainder 40,and apply the division lemma to get
42 = 40 x 1 + 2
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 454 and 784 is 2
Notice that 2 = HCF(40,2) = HCF(42,40) = HCF(82,42) = HCF(124,82) = HCF(330,124) = HCF(454,330) = HCF(784,454) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 2, we apply the division lemma to 22 and 2, to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 22 is 2
Notice that 2 = HCF(22,2) .
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Frequently Asked Questions on HCF of 454, 784, 22 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 454, 784, 22?
Answer: HCF of 454, 784, 22 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 454, 784, 22 using Euclid's Algorithm?
Answer: For arbitrary numbers 454, 784, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.