Highest Common Factor of 567, 7716, 9967 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 567, 7716, 9967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 567, 7716, 9967 is 1 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 567, 7716, 9967 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 567, 7716, 9967 is 1.
HCF(567, 7716, 9967) = 1
HCF of 567, 7716, 9967 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 567, 7716, 9967 is 1.
Highest Common Factor of 567,7716,9967 is 1
Step 1: Since 7716 > 567, we apply the division lemma to 7716 and 567, to get
7716 = 567 x 13 + 345
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 345 and 567, to get
567 = 345 x 1 + 222
Step 3: We consider the new divisor 345 and the new remainder 222, and apply the division lemma to get
345 = 222 x 1 + 123
We consider the new divisor 222 and the new remainder 123,and apply the division lemma to get
222 = 123 x 1 + 99
We consider the new divisor 123 and the new remainder 99,and apply the division lemma to get
123 = 99 x 1 + 24
We consider the new divisor 99 and the new remainder 24,and apply the division lemma to get
99 = 24 x 4 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 567 and 7716 is 3
Notice that 3 = HCF(24,3) = HCF(99,24) = HCF(123,99) = HCF(222,123) = HCF(345,222) = HCF(567,345) = HCF(7716,567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9967 > 3, we apply the division lemma to 9967 and 3, to get
9967 = 3 x 3322 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 9967 is 1
Notice that 1 = HCF(3,1) = HCF(9967,3) .
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Frequently Asked Questions on HCF of 567, 7716, 9967 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 567, 7716, 9967?
Answer: HCF of 567, 7716, 9967 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 567, 7716, 9967 using Euclid's Algorithm?
Answer: For arbitrary numbers 567, 7716, 9967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.