Highest Common Factor of 136, 778, 560 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 136, 778, 560 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 136, 778, 560 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 136, 778, 560 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 136, 778, 560 is 2.
HCF(136, 778, 560) = 2
HCF of 136, 778, 560 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 136, 778, 560 is 2.
Highest Common Factor of 136,778,560 is 2
Step 1: Since 778 > 136, we apply the division lemma to 778 and 136, to get
778 = 136 x 5 + 98
Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 98 and 136, to get
136 = 98 x 1 + 38
Step 3: We consider the new divisor 98 and the new remainder 38, and apply the division lemma to get
98 = 38 x 2 + 22
We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get
38 = 22 x 1 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 136 and 778 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(98,38) = HCF(136,98) = HCF(778,136) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 2, we apply the division lemma to 560 and 2, to get
560 = 2 x 280 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 560 is 2
Notice that 2 = HCF(560,2) .
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Frequently Asked Questions on HCF of 136, 778, 560 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 136, 778, 560?
Answer: HCF of 136, 778, 560 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 136, 778, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 136, 778, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
