Highest Common Factor of 501, 972, 688, 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 501, 972, 688, 22 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 501, 972, 688, 22 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 501, 972, 688, 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 501, 972, 688, 22 is 1.
HCF(501, 972, 688, 22) = 1
HCF of 501, 972, 688, 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 501, 972, 688, 22 is 1.
Highest Common Factor of 501,972,688,22 is 1
Step 1: Since 972 > 501, we apply the division lemma to 972 and 501, to get
972 = 501 x 1 + 471
Step 2: Since the reminder 501 ≠ 0, we apply division lemma to 471 and 501, to get
501 = 471 x 1 + 30
Step 3: We consider the new divisor 471 and the new remainder 30, and apply the division lemma to get
471 = 30 x 15 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 501 and 972 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(471,30) = HCF(501,471) = HCF(972,501) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 3, we apply the division lemma to 688 and 3, to get
688 = 3 x 229 + 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 688 is 1
Notice that 1 = HCF(3,1) = HCF(688,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 1, we apply the division lemma to 22 and 1, to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22 is 1
Notice that 1 = HCF(22,1) .
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Frequently Asked Questions on HCF of 501, 972, 688, 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 501, 972, 688, 22?
Answer: HCF of 501, 972, 688, 22 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 501, 972, 688, 22 using Euclid's Algorithm?
Answer: For arbitrary numbers 501, 972, 688, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.