Highest Common Factor of 560, 735, 508 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 560, 735, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 735, 508 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 560, 735, 508 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 560, 735, 508 is 1.
HCF(560, 735, 508) = 1
HCF of 560, 735, 508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 560, 735, 508 is 1.
Highest Common Factor of 560,735,508 is 1
Step 1: Since 735 > 560, we apply the division lemma to 735 and 560, to get
735 = 560 x 1 + 175
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 175 and 560, to get
560 = 175 x 3 + 35
Step 3: We consider the new divisor 175 and the new remainder 35, and apply the division lemma to get
175 = 35 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 560 and 735 is 35
Notice that 35 = HCF(175,35) = HCF(560,175) = HCF(735,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 35, we apply the division lemma to 508 and 35, to get
508 = 35 x 14 + 18
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 18 and 35, to get
35 = 18 x 1 + 17
Step 3: We consider the new divisor 18 and the new remainder 17, and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1, and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 35 and 508 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(35,18) = HCF(508,35) .
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Frequently Asked Questions on HCF of 560, 735, 508 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 560, 735, 508?
Answer: HCF of 560, 735, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 735, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 735, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.