Highest Common Factor of 560, 985, 970 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, 985, 970 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 985, 970 is 5 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, 985, 970 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, 985, 970 is 5.
HCF(560, 985, 970) = 5
HCF of 560, 985, 970 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, 985, 970 is 5.
Highest Common Factor of 560,985,970 is 5
Step 1: Since 985 > 560, we apply the division lemma to 985 and 560, to get
985 = 560 x 1 + 425
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 425 and 560, to get
560 = 425 x 1 + 135
Step 3: We consider the new divisor 425 and the new remainder 135, and apply the division lemma to get
425 = 135 x 3 + 20
We consider the new divisor 135 and the new remainder 20,and apply the division lemma to get
135 = 20 x 6 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 560 and 985 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(135,20) = HCF(425,135) = HCF(560,425) = HCF(985,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 970 > 5, we apply the division lemma to 970 and 5, to get
970 = 5 x 194 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 970 is 5
Notice that 5 = HCF(970,5) .
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Frequently Asked Questions on HCF of 560, 985, 970 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, 985, 970?
Answer: HCF of 560, 985, 970 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 985, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 985, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.