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 1652, 357 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 1652, 357 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 1652, 357 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 1652, 357 is 7.
HCF(1652, 357) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1652, 357 is 7.
Step 1: Since 1652 > 357, we apply the division lemma to 1652 and 357, to get
1652 = 357 x 4 + 224
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 224 and 357, to get
357 = 224 x 1 + 133
Step 3: We consider the new divisor 224 and the new remainder 133, and apply the division lemma to get
224 = 133 x 1 + 91
We consider the new divisor 133 and the new remainder 91,and apply the division lemma to get
133 = 91 x 1 + 42
We consider the new divisor 91 and the new remainder 42,and apply the division lemma to get
91 = 42 x 2 + 7
We consider the new divisor 42 and the new remainder 7,and apply the division lemma to get
42 = 7 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 1652 and 357 is 7
Notice that 7 = HCF(42,7) = HCF(91,42) = HCF(133,91) = HCF(224,133) = HCF(357,224) = HCF(1652,357) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 1652, 357?
Answer: HCF of 1652, 357 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1652, 357 using Euclid's Algorithm?
Answer: For arbitrary numbers 1652, 357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.