Highest Common Factor of 7560, 5613, 91872 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 7560, 5613, 91872 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7560, 5613, 91872 is 3 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 7560, 5613, 91872 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 7560, 5613, 91872 is 3.
HCF(7560, 5613, 91872) = 3
HCF of 7560, 5613, 91872 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7560, 5613, 91872 is 3.
Highest Common Factor of 7560,5613,91872 is 3
Step 1: Since 7560 > 5613, we apply the division lemma to 7560 and 5613, to get
7560 = 5613 x 1 + 1947
Step 2: Since the reminder 5613 ≠ 0, we apply division lemma to 1947 and 5613, to get
5613 = 1947 x 2 + 1719
Step 3: We consider the new divisor 1947 and the new remainder 1719, and apply the division lemma to get
1947 = 1719 x 1 + 228
We consider the new divisor 1719 and the new remainder 228,and apply the division lemma to get
1719 = 228 x 7 + 123
We consider the new divisor 228 and the new remainder 123,and apply the division lemma to get
228 = 123 x 1 + 105
We consider the new divisor 123 and the new remainder 105,and apply the division lemma to get
123 = 105 x 1 + 18
We consider the new divisor 105 and the new remainder 18,and apply the division lemma to get
105 = 18 x 5 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7560 and 5613 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(105,18) = HCF(123,105) = HCF(228,123) = HCF(1719,228) = HCF(1947,1719) = HCF(5613,1947) = HCF(7560,5613) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 91872 > 3, we apply the division lemma to 91872 and 3, to get
91872 = 3 x 30624 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 91872 is 3
Notice that 3 = HCF(91872,3) .
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Frequently Asked Questions on HCF of 7560, 5613, 91872 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 7560, 5613, 91872?
Answer: HCF of 7560, 5613, 91872 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7560, 5613, 91872 using Euclid's Algorithm?
Answer: For arbitrary numbers 7560, 5613, 91872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.