Highest Common Factor of 340, 572, 884, 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 340, 572, 884, 22 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 572, 884, 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 340, 572, 884, 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 340, 572, 884, 22 is 2.
HCF(340, 572, 884, 22) = 2
HCF of 340, 572, 884, 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 340, 572, 884, 22 is 2.
Highest Common Factor of 340,572,884,22 is 2
Step 1: Since 572 > 340, we apply the division lemma to 572 and 340, to get
572 = 340 x 1 + 232
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 232 and 340, to get
340 = 232 x 1 + 108
Step 3: We consider the new divisor 232 and the new remainder 108, and apply the division lemma to get
232 = 108 x 2 + 16
We consider the new divisor 108 and the new remainder 16,and apply the division lemma to get
108 = 16 x 6 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 340 and 572 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(108,16) = HCF(232,108) = HCF(340,232) = HCF(572,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 884 > 4, we apply the division lemma to 884 and 4, to get
884 = 4 x 221 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 884 is 4
Notice that 4 = HCF(884,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 4, we apply the division lemma to 22 and 4, to get
22 = 4 x 5 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 22 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) .
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Frequently Asked Questions on HCF of 340, 572, 884, 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 340, 572, 884, 22?
Answer: HCF of 340, 572, 884, 22 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 572, 884, 22 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 572, 884, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.