Highest Common Factor of 354, 484, 722 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 354, 484, 722 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 484, 722 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 354, 484, 722 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 354, 484, 722 is 2.
HCF(354, 484, 722) = 2
HCF of 354, 484, 722 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 484, 722 is 2.
Highest Common Factor of 354,484,722 is 2
Step 1: Since 484 > 354, we apply the division lemma to 484 and 354, to get
484 = 354 x 1 + 130
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 130 and 354, to get
354 = 130 x 2 + 94
Step 3: We consider the new divisor 130 and the new remainder 94, and apply the division lemma to get
130 = 94 x 1 + 36
We consider the new divisor 94 and the new remainder 36,and apply the division lemma to get
94 = 36 x 2 + 22
We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 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 354 and 484 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(94,36) = HCF(130,94) = HCF(354,130) = HCF(484,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 722 > 2, we apply the division lemma to 722 and 2, to get
722 = 2 x 361 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 722 is 2
Notice that 2 = HCF(722,2) .
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Frequently Asked Questions on HCF of 354, 484, 722 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 354, 484, 722?
Answer: HCF of 354, 484, 722 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 484, 722 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 484, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.