Highest Common Factor of 472, 8440, 5222 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 472, 8440, 5222 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 472, 8440, 5222 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 472, 8440, 5222 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 472, 8440, 5222 is 2.
HCF(472, 8440, 5222) = 2
HCF of 472, 8440, 5222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 472, 8440, 5222 is 2.
Highest Common Factor of 472,8440,5222 is 2
Step 1: Since 8440 > 472, we apply the division lemma to 8440 and 472, to get
8440 = 472 x 17 + 416
Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 416 and 472, to get
472 = 416 x 1 + 56
Step 3: We consider the new divisor 416 and the new remainder 56, and apply the division lemma to get
416 = 56 x 7 + 24
We consider the new divisor 56 and the new remainder 24,and apply the division lemma to get
56 = 24 x 2 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 472 and 8440 is 8
Notice that 8 = HCF(24,8) = HCF(56,24) = HCF(416,56) = HCF(472,416) = HCF(8440,472) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5222 > 8, we apply the division lemma to 5222 and 8, to get
5222 = 8 x 652 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: 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 8 and 5222 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(5222,8) .
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Frequently Asked Questions on HCF of 472, 8440, 5222 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 472, 8440, 5222?
Answer: HCF of 472, 8440, 5222 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 472, 8440, 5222 using Euclid's Algorithm?
Answer: For arbitrary numbers 472, 8440, 5222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.