Highest Common Factor of 7128, 7623, 34929 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 7128, 7623, 34929 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 7128, 7623, 34929 is 9 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 7128, 7623, 34929 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 7128, 7623, 34929 is 9.
HCF(7128, 7623, 34929) = 9
HCF of 7128, 7623, 34929 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7128, 7623, 34929 is 9.
Highest Common Factor of 7128,7623,34929 is 9
Step 1: Since 7623 > 7128, we apply the division lemma to 7623 and 7128, to get
7623 = 7128 x 1 + 495
Step 2: Since the reminder 7128 ≠ 0, we apply division lemma to 495 and 7128, to get
7128 = 495 x 14 + 198
Step 3: We consider the new divisor 495 and the new remainder 198, and apply the division lemma to get
495 = 198 x 2 + 99
We consider the new divisor 198 and the new remainder 99, and apply the division lemma to get
198 = 99 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 99, the HCF of 7128 and 7623 is 99
Notice that 99 = HCF(198,99) = HCF(495,198) = HCF(7128,495) = HCF(7623,7128) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34929 > 99, we apply the division lemma to 34929 and 99, to get
34929 = 99 x 352 + 81
Step 2: Since the reminder 99 ≠ 0, we apply division lemma to 81 and 99, to get
99 = 81 x 1 + 18
Step 3: We consider the new divisor 81 and the new remainder 18, and apply the division lemma to get
81 = 18 x 4 + 9
We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 99 and 34929 is 9
Notice that 9 = HCF(18,9) = HCF(81,18) = HCF(99,81) = HCF(34929,99) .
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Frequently Asked Questions on HCF of 7128, 7623, 34929 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 7128, 7623, 34929?
Answer: HCF of 7128, 7623, 34929 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7128, 7623, 34929 using Euclid's Algorithm?
Answer: For arbitrary numbers 7128, 7623, 34929 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
