Highest Common Factor of 980, 560, 752 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 980, 560, 752 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 980, 560, 752 is 4 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 980, 560, 752 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 980, 560, 752 is 4.
HCF(980, 560, 752) = 4
HCF of 980, 560, 752 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 980, 560, 752 is 4.
Highest Common Factor of 980,560,752 is 4
Step 1: Since 980 > 560, we apply the division lemma to 980 and 560, to get
980 = 560 x 1 + 420
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 420 and 560, to get
560 = 420 x 1 + 140
Step 3: We consider the new divisor 420 and the new remainder 140, and apply the division lemma to get
420 = 140 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 140, the HCF of 980 and 560 is 140
Notice that 140 = HCF(420,140) = HCF(560,420) = HCF(980,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 752 > 140, we apply the division lemma to 752 and 140, to get
752 = 140 x 5 + 52
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 52 and 140, to get
140 = 52 x 2 + 36
Step 3: We consider the new divisor 52 and the new remainder 36, and apply the division lemma to get
52 = 36 x 1 + 16
We consider the new divisor 36 and the new remainder 16,and apply the division lemma to get
36 = 16 x 2 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 140 and 752 is 4
Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(52,36) = HCF(140,52) = HCF(752,140) .
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Frequently Asked Questions on HCF of 980, 560, 752 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 980, 560, 752?
Answer: HCF of 980, 560, 752 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 980, 560, 752 using Euclid's Algorithm?
Answer: For arbitrary numbers 980, 560, 752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
