Highest Common Factor of 987, 770, 553 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 987, 770, 553 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 770, 553 is 7 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 987, 770, 553 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 987, 770, 553 is 7.
HCF(987, 770, 553) = 7
HCF of 987, 770, 553 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 987, 770, 553 is 7.
Highest Common Factor of 987,770,553 is 7
Step 1: Since 987 > 770, we apply the division lemma to 987 and 770, to get
987 = 770 x 1 + 217
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 217 and 770, to get
770 = 217 x 3 + 119
Step 3: We consider the new divisor 217 and the new remainder 119, and apply the division lemma to get
217 = 119 x 1 + 98
We consider the new divisor 119 and the new remainder 98,and apply the division lemma to get
119 = 98 x 1 + 21
We consider the new divisor 98 and the new remainder 21,and apply the division lemma to get
98 = 21 x 4 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 987 and 770 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(98,21) = HCF(119,98) = HCF(217,119) = HCF(770,217) = HCF(987,770) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 553 > 7, we apply the division lemma to 553 and 7, to get
553 = 7 x 79 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 553 is 7
Notice that 7 = HCF(553,7) .
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Frequently Asked Questions on HCF of 987, 770, 553 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 987, 770, 553?
Answer: HCF of 987, 770, 553 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 770, 553 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 770, 553 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.