Highest Common Factor of 756, 9994, 3570 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 756, 9994, 3570 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 9994, 3570 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 756, 9994, 3570 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 756, 9994, 3570 is 2.
HCF(756, 9994, 3570) = 2
HCF of 756, 9994, 3570 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 9994, 3570 is 2.
Highest Common Factor of 756,9994,3570 is 2
Step 1: Since 9994 > 756, we apply the division lemma to 9994 and 756, to get
9994 = 756 x 13 + 166
Step 2: Since the reminder 756 ≠ 0, we apply division lemma to 166 and 756, to get
756 = 166 x 4 + 92
Step 3: We consider the new divisor 166 and the new remainder 92, and apply the division lemma to get
166 = 92 x 1 + 74
We consider the new divisor 92 and the new remainder 74,and apply the division lemma to get
92 = 74 x 1 + 18
We consider the new divisor 74 and the new remainder 18,and apply the division lemma to get
74 = 18 x 4 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 756 and 9994 is 2
Notice that 2 = HCF(18,2) = HCF(74,18) = HCF(92,74) = HCF(166,92) = HCF(756,166) = HCF(9994,756) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3570 > 2, we apply the division lemma to 3570 and 2, to get
3570 = 2 x 1785 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 3570 is 2
Notice that 2 = HCF(3570,2) .
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Frequently Asked Questions on HCF of 756, 9994, 3570 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 756, 9994, 3570?
Answer: HCF of 756, 9994, 3570 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 9994, 3570 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 9994, 3570 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.